case study questions on lcm and hcf class 6

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LCM and HCF questions for class 6 worksheet and PDF Download

Finding HCF is a  fundamental concept  of mathematics. For Class 6 students, grasping the idea of HCF is a crucial step in building a strong foundation in math. In this blog, we’ll explore HCF and provide some HCF questions to help you practice and understand it better.

What is the Highest Common Factor (HCF)?

The Highest Common Factor, or HCF, is the largest number that divides two or more numbers without leaving any remainder. It’s also known as the Greatest Common Divisor (GCD).

Why is HCF Important?

Understanding HCF is essential because it forms the basis for various mathematical concepts and real-life problem-solving situations. Here are a few reasons why HCF is important:

• Simplifying Fractions: Knowing the HCF of two numbers helps you simplify fractions. For instance, the HCF of 4 and 6 is 2, so you can simplify 4/6 to 2/3.
• Common Multiples: HCF is also useful in finding common multiples. It allows you to find the least common multiple (LCM), which is valuable in various mathematical operations.
• Word Problems: In everyday life, you might encounter scenarios where you need to divide something equally among a group of people. HCF helps you determine the largest group size without any leftovers.

Properties of HCF:

• The HCF of two or more numbers exactly divides the numbers.
• The HCF of given numbers can not be greater than the numbers themselves
• If one number is a factor  of another number, the smaller number is the HCF.
• If the HCF of two numbers is 1, they are called co-prime numbers.
• Consecutive numbers are always co-prime. For example 7 and 8,  13 and 14  are co-prime numbers.

Lowest Common Multiple(LCM)

The lowest common multiple  of two or more numbers is the smallest of their common multiples.

Properties of LCM :

• The LCM of two or more numbers is the smallest number that  is completely divisible by each of the numbers.
• The LCM of two or more numbers can not be less than the numbers themselves.
• If one number is the factor of the other, the greatest number is the LCM.
• The LCM of co-prime is their product. For example LCM of 3 and 5 is 15.

Relation between HCF and LCM

HCF Questions for Class 6 (Solved examples)

Let’s practice with a few HCF questions to solidify our understanding:

(I)Find the  HCF of 24 and 32 by Factorization method. 

Sol. We have: 24=1 x 24 ; 24=2 x 12 ;  24= 3 x 8 and  24= 4 x 6

Again , 32= 1 x 32;   32= 2 x 16;    32= 4 x 8

Common factors of 24 and 32 are : 1, 2, 4, 8

(II) Find the HCF of 72 and 90 by prime factorization method. 

Sol. By prime factorization , we have  :  72= 2 x 2 x 2 x 3 x 3 ,  90= 2 x 3 x 3 x 5

= 2 x 3 x 3

Hence , the HCF  of 72 and 90  is 18.

(III) Find the HCF of 135 and 180  by division method.

(IV) Find the HCF of 217 , 385 and 735 by division method.

Sol. First , we find the HCF of 217 and 385.

Clearly, 7 divides 735 completely, so the HCF of 7 and 735 is 7. Hence HCF of 217 , 385 and 735 is 7.

(V)Two buckets contain 15 litres and 25 litres of water. Find the maximum capacity of a mug that can exactly measure the water in both the buckets.

Sol. The maximum capacity of a mug will be the HCF of  15 and 25.

So, the HCF of 15 and 25 is 5.

Hence , the  maximum capacity  of a mug  is 5 litres.

(VI)Two ropes, one 8 meters long and the other 12 meters long are to be cut into pieces of the same length. What will the maximum possible length of each piece be ?

Sol.  The maximum possible length of each piece of rope of the same length that can be cut from the two given ropes is the HCF of 8 m and 12 m.

8 = 2 x 2 x 2

12 = 2 x 2 x 3

So the HCF of  8 and 12 is  2 x 2 =4.  (taking common factors only once)

Thus, the maximum possible length of each piece of rope is 4 m.

(VII) Find the greatest number which divides 148 and 100 leaving remainder 4 in each case.

Sol.   Clearly, we have to find the largest number  that divides (148-4)  i.e. 140  and (100-4) i.e.  96 exactly.

Prime factor of 144 and 96 are

144= 2 x 2 x 2 x 2 x 3 x 3

96= 2 x 2 x 2 x 2 x 2 x 3  

Hence the required number is 48.

LCM questions for class 6

(VIII) Find the LCM of 90, 108 and 144 by prime factorization method.

Sol.  Finding prime factors of each of the given numbers, we get :

90= 2 x 3 x 3 x 5 ;           108= 2 x 2 x 3 x 3  x 3 ;                144 = 2 x 2 x 2 x 2 x 3 x 3

The prime factor 2 appears maximum four times, the prime factor 3 appears maximum three times  and  the prime factor 5 appears  maximum one time, so the required LCM is

(IX) Find the LCM and HCF of 680 and 816.

Sol. Prime factorisation of 680 and 816 are

680= 2 x 2 x 2 x 5 x 17

816= 2 x 2 x 2  x 2 x 3 x 17

So, the HCF of 680 and 816 is = 2 x 2 x 2 x 17= 136

So LCM= 4080

(X) Find the LCM of  96, 108 and 180 by short division method.

(XI)  Find the LCM of 40, 48 and 45   by prime factorisation. Sol. The prime factorisation of 40, 48 and 45 are; 40 = 2 × 2 × 2 × 5 48 = 2 × 2 × 2 × 2 × 3 45 = 3 × 3 × 5 The prime factor 2 appears maximum number of four times in the prime factorization of 48, the prime factor 3 occurs maximum number of two times in the prime factorization of 45, The prime factor 5 appears one time in the prime factorisation of 40 and 45, Therefore, required LCM = (2 × 2 × 2 × 2)×(3 × 3) × 5 = 720.

(XII)  Find the least number which when divided by 12, 16, 24 and 36 leaves a remainder 7 in each case. Sol. We first find the LCM of 12, 16, 24 and 36 as follows :

Thus, LCM = 2 × 2 × 2 × 2 × 3 × 3 = 144.

144 is the least number which when divided by the given numbers will leave  remainder 0 in each case. But we need the least number that leaves remainder 7 in each case.   Therefore, the required number is 7 more than 144.

Hence , the required least number = 144 + 7 = 151.

LCM and HCF questions for class 6 (Unsolved examples with answers)

(i) Find the HCF of the following numbers: (a) 11, 44         (b) 35, 42         (c) 128, 60        (d) 81, 63      (e) 36, 180      (f) 1152, 1664

(ii) Find the HCF by finding all the factors.

(a)36, 48, 96     (b) 31, 37, 33        (c) 64, 74, 84

(iii) Find the HCF by prime factorisation.

(a)30, 45, 75    (b) 27, 30       (c) 18, 64, 80

(iv)Find the HCF by long division method.

(a)16 , 20       (b) 35, 95     (c) 65, 135

(v)Find the HCF of 70, 105, 175 .

(vi)Two buckets contain 15 litres and 25 litres of water. Find the maximum capacity of a mug that can exactly measure the water in both the buckets.

(vii)Two ropes, one 8 metres long and the other 12 metres long are to be cut into pieces of the same length. What will the maximum possible length of each piece be ?

(viii)The number of students of Std 6th and Std 7th who went to visit the Tadoba Tiger Project at Chandrapur was 140 and 196 respectively. The students of each class are to be divided into groups of the same number of students. Each group can have a paid guide. What is the maximum number of students there can be in each group ?

(ix)At the Rice Research Centre at Tumsar, there are 2610 kg of seeds of the basmati variety and 1980 kg of the Indrayani variety. If the maximum possible weight of seeds has to be filled to make bags of equal weight what should be the weight of each bag ? How many bags of each variety will there be ?

(x)Three pieces of timber 42m, 49m and 63m long have to be divided into planks of the same length. What is the greatest possible length  of each plank?

Ans. (i) (a) 11       (b) 7       (c) 4   (d) 9   (e) 12   (f) 128   (ii) (a ) 12     (b) 1       (c) 2      (iii) (a) 15     (b) 3      ( c) 2  (iv ) (a) 4       (b) 5      (c )5       (v) 35     (vi) 5 litres     (vii)4 m  (viii)28 students    (ix)  maximum weight of each bag should be 90 kg,   Number of bags filled with the seeds of basmati rice = 29 ,  Number of bags filled with the seeds of Indrayani rice= 22      (x)7m

LCM questions for class 6 (unsolved with answers)

(i) Find the LCM of 20, 30 and 50 by short division method.

(ii)Find the LCM of 96, 108 and 180 by short division method.

(iii) Find the LCM of 48 and 72 by prime factorization.

(iv)Four bells begin to toll together and toll respectively at intervals of 6, 7, 8 and 12 seconds. After how much time will they toll together again?

(v)What is the least number of children that can be arranged in rows of 10, 15 or 25 children in each row?

(vi)Find the LCM by the short division method.

(a) 30, 55       (b) 9 , 27      (c) 20, 65    (d) 10, 15, 25    (e)27, 54, 63

(vii)Find the LCM by prime factorisation method.

(a)24, 36     (b) 18, 27    (c) 40 , 32    (d) 21, 14, 42   (e) 10, 15, 18

(viii)Find the LCM of 12, 18, 24 and 36 by short division method.

(ix)Find the least number which is exactly divisible by each one of the numbers 12, 16 and 24.

(x) Find the least number of stones so that heaps of 15, 20 and 30 stones can be made.

Ans.  (i) 300     (ii) 4320     (iii) 144   (iv)  2 min. 48 sec   (v) 150     (vi) (a) 330    (b) 27     (c) 260   (d) 150   (e) 378    (vii) (a) 72   (b) 54  (c) 160   (d) 42    (e) 90    (viii) 72     (ix)   48       (x) 60

LCM and HCF questions for class 6 worksheet and PDF

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Course: up class 6th (bridge)   >   unit 1, hcf and lcm product.

• Relationship between HCF and LCM
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HCF and LCM

CBSE Class 6 Mathematics Chapter-3 Playing with numbers- HCF and LCM. HCF refers to the highest common factor and LCM refers to least common factor.

CBSE Class 6 Mathematics Notes

Read More related topics…..

Introduction to Factors and Multiples

Factors and Common Factors

Properties of Factors

Multiples and Properties of Multiples

Prime and Composite Numbers

Eratosthenes Sieve to Find Prime Numbers

Co-Prime Numbers

Test of Divisibility

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6th Class Mathematics Fractions Question Bank

Done lcm and hcf total questions - 40.

question_answer 1) Which one among the following statements is not true?

A) The LCM of two or more given numbers is the lowest of their common multiple. done clear

B) The HCF of two or more given numbers is the highest of their common factors. done clear

C) The numbers having more than two factors are called coprime numbers. done clear

D) All the above done clear

E) None of these done clear

question_answer 2) The ratio between two numbers is 8:5 and their LCM is 360. The larger number is___.

A) 24 done clear

B) 72 done clear

C) 48 done clear

D) 36 done clear

question_answer 3) Which one among the following is most appropriate for coprimes?

A) Numbers having more than two factors are called coprimes. done clear

B) Two numbers are called coprimes, if there is no common factor other than 1, between these two numbers. done clear

C) Two numbers are called coprimes, if there is no common factor other than 2, between these two numbers. done clear

D) Pair of prime numbers are called coprimes. done clear

question_answer 4) The least number which when divided by 4, 5 and 6 leaves remainder 3 in each case, is_____.

A) 63 done clear

B) 67 done clear

C) 71 done clear

D) 252 done clear

question_answer 5) Find the LCM of 9, 14, 15, 18, 12.

A) 126 done clear

B) 252 done clear

C) 630  done clear

D) 1260 done clear

question_answer 6) The LCM of three prime numbers are 4991. Find the between these prime numbers,

A) 47 done clear

B) 19 done clear

C) 29 done clear

D) 31 done clear

question_answer 7) The LCM of two numbers is 27. The numbers cannot be____.

A) 3, 27 done clear

B) 1. 27 done clear

C) 3, 9 done clear

D) 9, 27 done clear

question_answer 8) The HCF of two numbers is 48. The product of the numbers can be___.

A) 3200 done clear

B) 2400 done clear

D) 4608 done clear

question_answer 9) The product of two numbers is 324. Their HCF can be______.

A) 54 done clear

B) 9 done clear

C) 4 done clear

D) 27 done clear

question_answer 10) The product of two numbers is 840. Their LCM can be

A) 210 done clear

B) 70 done clear

C) 420 done clear

question_answer 11) The HCF and LCM of the numbers 780 and 210 are respectively ___

A) 30, 5460 done clear

B) 60, 2730 done clear

C) 90, 10920 done clear

D) 30, 2730 done clear

question_answer 12) A rectangular courtyard with length 10m 50cm and breadth 4m 20cm is to be paved with square stones of the same size. The least number of such stones required are___.

A) 20 done clear

B) 10 done clear

C) 8  done clear

D) 6 done clear

question_answer 13) Least common multiple number of two numbers is 360. Then which one of the following cannot be the highest common factor of the numbers.

A) 36 done clear

B) 24 done clear

C) 16 done clear

D) 15 done clear

question_answer 14) Find the LCM of the numbers 10, 7, 8, 11, 52, 27.

A) 1181820 done clear

B) 1081080 done clear

C) 2162160 done clear

D) 540540 done clear

question_answer 15) The least common multiple of four numbers is 720. If three numbers are 16, 10 and 40 then fourth number can be _______.

A) 75  done clear

B) 144 done clear

C) 80 done clear

D) 54 done clear

question_answer 16) The product of two numbers is 11016 and their HCF is 18. Find their LCM.

A) 1224     done clear

B) 612 done clear

C) 112 done clear

D) 560 done clear

question_answer 17) The HCF of the greatest two digit prime numbers and the greatest four digit numbers is ___

A) 195 done clear

B) 199 done clear

C) 1 done clear

D) 97 done clear

question_answer 18) The sum of two numbers is 324 and their HCF is 9. Find the numbers.

A) 18, 306  done clear

B) 315, 9 done clear

C) 27, 297 done clear

question_answer 19) The HCF and LCM of two numbers are 28 and 1176 respectively. If the difference between the numbers is 308, then the numbers can be

A) 1176, 28 done clear

B) 412, 104 done clear

C) 392, 84 done clear

D) 402, 94 done clear

question_answer 20) Swapnesh wants to mail three parcels to three village schools. He finds that the postal charges are Rs 42, Rs 63 and Rs 294. He wants to buy stamps only of one denomination. Find the greatest denomination of stamps he must buy to mail the three parcels.

A) 23 done clear

B) 21 done clear

C) 27 done clear

question_answer 21) The HCF of two numbers is 35 and the other two factors of their LCM are 11 and 17. Find the larger of the two numbers.

A) 595 done clear

B) 365 done clear

C) 275 done clear

D) 385 done clear

question_answer 22) Six bells are tolled together They toil at the  of 3, 5, 8, 9, 12 and 15 seconds respectively in 24 hours, how many times do they toll together?

A) 4  done clear

B) 120 done clear

C) 12 done clear

D) 240 done clear

question_answer 23) In a school library there are 1080 books of Mathematics and 792 books of Science. Ms Shilpi, the librarian of the school wants to store these books in shelves such that each shelf should have the same number of books of each subject. What should be the minimum number of each subject in each shelf?

A) 72 done clear

B) 36 done clear

C) 108   done clear

D) 2310 done clear

question_answer 24) The product of two numbers is 9126. If HCF of the numbers is 39, find the larger numbers.

A) 39 done clear

B) 78 done clear

C) 156  done clear

D) 117 done clear

question_answer 25) HCF of two numbers is 42. If the product of the numbers is 15876, then possible number of such pairs is_______

A) 1 done clear

B) 2 done clear

C) 3 done clear

D) 4 done clear

question_answer 26) The least multiple of 7 which leaves a remainder of 5 when divided by 13, 15, 18 and 36, is____.

A) 2345 done clear

B) 235 done clear

C) 335  done clear

D) 2340 done clear

question_answer 27) Three tankers can contain 391 litres, 483 litres and 667 litres of diesel respectively. Find the maximum capacity of a container which can measure the diesel of the three containers exact number of times,

A) 17 litres  done clear

B) 21 litres done clear

C) 23 litres  done clear

D) 29 litres done clear

question_answer 28) The least number which when doubled will be exactly divisible by 24, 16, 21 and 28 is ____.

A) 336    done clear

B) 168 done clear

C) 672 done clear

D) 330 done clear

question_answer 29) The smallest 5 digit number exactly divisible by 6, 7, 8, 9and 10 is ____.

A) 10080 done clear

B) 25200 done clear

C) 10008   done clear

D) 10540 done clear

question_answer 30) Find the least possible length which can exactly measure the lengths 12 m, 14 m 85 cm and 10 m 8 cm.

A) 8316 m  done clear

B) 3456 m done clear

C) 5468 m done clear

D) 6902 m done clear

question_answer 31) The HCF of 2.59, 6.29 and 3.7 is _____.

A) 0.74 done clear

B) 7.4 done clear

C) 0.37   done clear

D) 3.7 done clear

question_answer 32) The LCM of 174, 319 and 377 is _____.

A) 24882 done clear

B) 24412 done clear

C) 329246  done clear

D) 29264 done clear

question_answer 33) Which of the following statements is correct?

A) The HCF of two distinct prime numbers is not 1. done clear

B) The HCF of two co prime numbers is not 1. done clear

C) The HCF of an even and odd number is not even. done clear

D) The HCF of two consecutive odd numbers is not 1. done clear

question_answer 34) The greatest number which on dividing 6997 and 5222, leaves a remainder of 12 and 15 respectively, is _____.

A) 127 done clear

B) 129 done clear

C) 133 done clear

D) 141 done clear

question_answer 35) The largest number which divides 625,856 and 1626 to leave the same remainder, is _____.

A) 33 done clear

C) 77 done clear

D) 147 done clear

question_answer 36) Six bells commence tolling together and toll at the intervals of 3, 5, 8, 10, 12 and 15 seconds respectively in 2 hours. How many times they will toll together?

A) 30 done clear

B) 12 done clear

C) 60 done clear

D) 1 done clear

question_answer 37) If the ratio of two numbers is 5: 6 and their HCF is 8, then find their LCM.

A) 300 done clear

C) 240 done clear

D) 160 done clear

question_answer 38) If the product of two numbers is 1259712 and their HCF is 27 then find their LCM.

A) 46656 done clear

B) 48658 done clear

C) 52560 done clear

D) 38902 done clear

question_answer 39)   Among three co-prime numbers, the product of the first two is 18304 and the product of the last two is 72576, find the sum of these numbers.

A) 588 done clear

B) 764 done clear

C) 686 done clear

D) 838 done clear

question_answer 40) Find the HCF of\[\frac{2}{3},\frac{10}{9},\frac{4}{15}\].

A) \[\frac{1}{9}\] done clear

B) \[\frac{2}{45}\]  done clear

C) \[\frac{1}{33}\]    done clear

D) \[\frac{1}{18}\] done clear

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• LCM and HCF

NCERT curriculum (for CBSE/ICSE) Class 6 - LCM and HCF

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Contents: LCM and HCF

LCM and HCF - Questions on LCM and HCF/GCD

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HCF and LCM Worksheet-1

• What is the HCF of 34 and 102?

(a) 102                (b) 34                 (c) 17                   (d) 1

• 'A' and 'B' tankers contain 840 litres and 420 litres of oil, respectively. What is the maximum capacity of a container which can measure the oil of both the tankers an exact number of times?

(a) 840 litres    (b) 20 litres       (c) 40 litres       (d) 420 litres

• Which one of the following statements is correct?

(a) Every factor is less than or equal to the given numbers.

(b) Every factor is always less than the given numbers.

(c) Every factor is always greater than the given numbers.

(d) Every factor is always equal to the given numbers.

• Find the largest divisor that divides 47, 80 and 124, and leaves remainder 3.

(a) 12                  (b) 11                   (c) 10                  (d) 3

• What is G.C.D of 4 and 15?

(a) 0                    (b) 4                    (c) 3                    (d) 1

• What is the G.C.F of two consecutive numbers?

(a) 2                    (b) 4                    (c) 1                     (d) 3

• A factor of a number is an ____ of that number.

Select the right word to be filled in the blank space from the following options.

(a) Exact multiple.                       (b) Exact Quotient.

(c) Exact divident.                        (d) Exact divisor.

• Find the largest number that will divide 623, 729 and 841 leaving remainders 3, 9 and 1 respectively?

(a) 45                  (b) 36                 (c) 20                  (d) 72

• A rectangular plastic sheet is 4,032 cm long and 3,040 cm broad. It is to be cut into square pieces of the same size. Find the maximum length of the each square piece?

(a) 16 cm           (b) 32 cm           (c) 40 cm           (d) 34 cm

• A hall of size 20.8 m by 16.8 m, has to be covered with white square tiles of same sizes. What is the length of the largest square tile that can be laid in the hall?

(a) 10 cm           (b) 12 cm           (c) 8 cm             (d) 16 cm

Answer Key:

LCM Questions

LCM Questions are given here, along with detailed solutions and proper explanations to help out students regarding the concept of LCM. These questions on LCM will help the students to be able to solve the problems efficiently. Learn more about What is LCM?

The LCM or Lowest Common Multiple of two or more numbers is the least among all the common multiples of given numbers. For example, LCM of 2, 4 and 5 is 20, which is the lowest common multiple of 2, 4 and 5, or we can say 20 is the lowest number which 2, 4 and 5 can divide.

LCM Questions with Solutions

1. If HCF(252, 594) = 18, find LCM(252, 594).

Solution: We have LCM of two numbers = (Product of two numbers)/ their HCF

= (252 × 594)/18 = 8316.

Hence, LCM(252, 594) = 8316

2. Player 1 and player 2 are running around a circular field. Player 1 takes 16 minutes to take one round, while Player 2 completes the round in 20 minutes. If both start simultaneously and go in the same direction, after how much time will they meet at the starting point?

Solution: Time taken by the players to meet again = LCM(16, 20)

Now 16 = 2 4 and 20 = 2 2 × 5

Therefore, LCM(16, 20) = 2 4 × 4 = 80

Hence, both will meet at the starting point after 80 minutes.

3. Is it possible to have two numbers whose HCF is 18 and LCM is 540?

Solution: Since HCF always divides LCM, we see that 540 is divisible by 18, 540/18 = 30.

Thus, it is possible to have two numbers.

4. Find the least number divided by 28 and 32, leaving the remainder 8 and 12, respectively.

Solution: Since 28 – 8 = 20 and 32 – 12 = 20

So we need LCM{(28, 32) – 20} = 224 – 20 = 204

Thus, 204 is required number.

5. Find the least number, which, when divided by 35, 56 and 91, leaves the same remainder of 7, respectively.

Solution: Let us find LCM(35, 56, 91) + 7

56 = 2 × 2 × 2 × 7

91 = 7 × 13

Thus, LCM(35, 56, 91) = 2 3 × 5 × 7 × 13 = 3640

The required number = LCM(35, 56, 91) + 7 = 3640 + 7 = 3647.

6. Two alarm clocks ring their alarms at regular intervals of 72 seconds and 50 seconds. If they beep together at noon, at what time will they beep again for the first time?

Solution: We find the LCM of 72 and 50.

Prime factorisation of 72 and 50,

72 = 2 × 2 × 2 × 3 × 3

50 = 2 × 5 × 5

Therefore, the LCM of 72 and 50 = 2 3 × 3 2 × 5 2 = 1800

1800 seconds = 1800/60 min = 30 min

Hence, the clocks will beep again for the first time at 12:30 pm.

7. There are 56 students in section A and 58 students in section B of a class in a school. Find the minimum number of books required for their class library so that they can be distributed equally among the students of section A or section B.

Solution: Clearly, the number of books that are to be equally distributed should be multiple of 56 and of 58. Thus, we have to find LCM of 56 and 58.

Now, 56 = 2 × 2 × 2 × 7

58 = 2 × 29

LCM (56, 58) = 2 3 × 7 × 29 = 1624.

Hence, atleast 1624 books are required in the library.

• Euclid’s Division Lemma
• Real Numbers
• Rational and Irrational Numbers
• Polynomials

8. Find the LCM of 96(x – 1)(x + 1) 2 (x + 3) 3 and 64(x 2 – 1)(x + 3)(x + 2) 2 .

Solution: Let f(x) = 96(x – 1)(x + 1) 2 (x + 3) 3

And g(x) = 64(x 2 – 1)(x + 3)(x + 2) 2

Now, factorising the polynomials into irreducible factors.

f(x) = 2 × 2 × 2 × 2 × 2 × 3 × (x – 1)(x + 1) 2 (x + 3) 3

g(x) = 2 × 2 × 2 × 2 × 2 × 2 × (x + 1)(x – 1)(x + 3)(x + 2) 2

Taking all the factors raised to their highest exponents: 2 6 , 3, (x – 1), (x + 1) 2 , (x + 3) 3 , (x + 2) 2

⇒ The LCM of the given polynomials = 192(x – 1)(x + 1) 2 (x + 2) 2 (x + 3) 3 .

9. Find the LCM of ⅔, ¾ and 7/2.

Solution: LCM of ⅔, ¾ and 7/2 = [LCM of (2, 3, 7)]/[HCF of (3, 4, 2)]

LCM of (2, 3, 7) = 2 × 3 × 7 = 42

HCF of (3, 4, 2) = 1

Therefore, LCM of ⅔, ¾ and 7/2 = 42.

10. Find the LCM of 22.5, 3.5 and 0.55.

Solution: Converting the decimals into integers,

22.5 = 22.5 × 100 = 2250

3.5 = 3.5 × 100 = 350

0.55 × 100 = 55

Now, 2250 = 2 × 3 × 3 × 5 × 5 × 5

350 = 2 × 5 × 5 × 7

55 = 5 × 11

LCM (225, 350, 55) = 2 × 3 2 × 5 3 × 7 × 11 = 173250

Place a decimal point after place from right

Then, LCM(22.5, 3.5, 0.55) = 1732.5.

11. Find the smallest number, which is, when reduced by 7, is divisible by 12, 16, 18, 21 and 28.

Solution: Let x be a number when reduced by 7, is divisible by 12, 16, 18, 21 and 28.

Then, x – 7 = m × 12 ⇒ x = m × 12 + 7.

Thus, when x is divided by 12, it leaves a remainder of 7, which is the same for each given number.

∴ x = LCM (12, 16, 18, 21, 28) + 7 = 1008 + 7 = 1015.

12. Find the largest four-digit number, which is divided by 4, 7 and 13, leaving a remainder of 3, respectively.

Solution: Largest 4-digit number = 9999

LCM (4, 7, 13) = 364

Now 9999 = 27 × 364 + 171

Thus, the 4-digit number divisible by 4, 7 and 13 = 9999 – 171 = 9828.

Since the number we have to find leaves a remainder of three when divided by 4, 7 and 13,

∴ 9828 + 3 = 9831 is the required number.

13. Six bells commence tolling together. After that, they toll at a time interval of 2, 4, 6, 8, 10 and 12 seconds, respectively. In 60 minutes, how many times do they toll together?

Solution: Taking LCM (2, 4, 6, 8, 10, 12) = 120

So, the bells will toll together after each 120 seconds = 2 min

∴ In 60 minutes number of times the bells will toll = 60/2 + 1 = 31 times.

Video Lesson on Application of LCM

Related Articles:

Practice questions:.

1. If the LCM of 12x 3 y 2 and 18x p y 3 is 36x 4 y 3 . Find the value of p.

2. The sum of LCM and HCF of the two numbers is 1260. If their LCM is 900 more than their HCF, find the product of two numbers.

3. The LCM and HCF of two numbers are equal; the numbers must be ______.

4. Two bells toll at an interval of 24 minutes and 36 minutes, respectively. If they tolled together at 9 am, after how many minutes do they toll together again, at the earliest?

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MCQ Questions for Class 6 ICSE Maths HCF and LCM (Online Available)

Free mcq test, table of content, hcf and lcm test - 1.

Duration: 20 Mins

Maximum Marks: 20

Read the following instructions carefully.

1. The test contains 20 total questions.

2. You have to finish the test in 20 minutes.

3. You will be awarded 1 mark for each correct answer.

4. There is no negative marking.

5. You can view your Score & Rank after submitting the test.

6. Check detailed Solution with explanation after submitting the test.

7. Rank is calculated on the basis of Marks Scored & Time

Many students believe that attempting MCQ questions for Class 6 ICSE Maths HCF and LCM is quite easy; but they need to complete the chapter in a proper way then only they can score well. To score well, students need to select the accurate options from the 4 or 5 options which can be easy or tricky; selecting the accurate option requires understanding of HCF and LCM questions, identifying the keywords and obviously eliminating the wrong option. 

Online MCQ Questions for Class 6 ICSE Maths HCF and LCM

While attempting MCQ questions for Class 6 ICSE Maths HCF and LCM students need to learn the right approach; to learn the right approach, they can refer to Selfstudys website which is available in the online mode. Students should prefer online mode so that they can practiseHCF and LCM questions from their comfort zone and can get instant feedback to improve. 

How to Attempt MCQ Questions for Class 6 ICSE Maths HCF and LCM? 

To attempt the ICSE MCQ Questions for Class 6 Maths HCF and LCM in the online mode, students can follow the given steps: 

• Open the Selfstudys website.

• Search for Free Study Materials from the website.

• Now click CISCE and select MCQ Test from the list. 

• A new page will appear and select Class 6 from the list of classes. 
• A drop down menu will appear, select HCF and LCM from the list of chapters. 

Everything Students Need to Know Before Solving MCQ Questions for Class 6 ICSE Maths HCF and LCM

Before solving MCQ questions for Class 6 ICSE Maths HCF and LCM, they need to know everything about it so that can solve effectively, some of the attributes are discussed below: 

• Provides Simple Language: Language in the Class 6 ICSE Maths HCF and LCM MCQ questions are very simple so that students can also understand difficult questions. 
• Answer Keys are Given: In the MCQ questions of Class 6 HCF and LCM, answer keys are given so that students can refer to whenever they are in a doubt. 
• Details for Time Taken is Provided: It is important for students to know how much time they have taken to complete HCF and LCM MCQ questions for Class 6; for this purpose they can refer to the Selfstudys website. 
• Available Online: The MCQs of Class 6 HCF and LCM are available online that is students can easily practise from their comfort zone. 
• Score is Given: Score is considered to be the points awarded for student’s performance; the same is given after attempting MCQs of Class 6 HCF and LCM. 
•  Question Analysis are Given: In the MCQs of ICSE Class 6 HCF and LCM, questions analysis are given; through the analysis students can get to know about answered, unanswered, skipped questions. 

Exploring the Benefits of MCQ Questions for Class 6 ICSE Maths HCF and LCM

The word for exploring the benefits is to search around the benefits of solving MCQ questions for Class 6 ICSE Maths HCF and LCM, some of the benefits are discussed below: 

• Comprehensive Coverage: Comprehensive coverage means which includes all the topics and concepts of a chapter; the same is followed through the Class 6 ICSE Maths HCF and LCM MCQ questions. 
• Familiarises the Exam Format: As we all know that MCQ questions of Class 6 HCF and LCM have 4 options and students need to select the accurate option from it; they can get familiarised with this format by regular practise. 
• Reduces the Number of Silly Mistakes: By practising HCF and LCM MCQ questions for Class 6, students can decrease the anxiety level; accordingly they can reduce the number of silly mistakes which generally happens due to increased anxiety level. 
• Helps in Revision: When students solve MCQs of HCF and LCM, they eventually end up covering most important topics and concepts; so it is obvious that they can revise all concepts. 
•  Builds Confidence: Solving maximum MCQs of HCF and LCM can help students to build confidence as it trains students to approach questions in different ways. 
• Saves Time: Students just need to select the accurate options in the multiple choice questions of Class 6 HCF and LCM which can save most of time and can be utilised to attempt other questions. 

How to Ace MCQ Questions for Class 6 ICSE Maths HCF and LCM?

Students should follow strategies to ace in MCQ questions for Class 6 ICSE Maths HCF and LCM, those strategies are discussed below: 

• Understand the Concepts: Before attempting Class 6 ICSE Maths HCF and LCM MCQ questions, students should make sure that they have understood each and every concept. 
• Pay Attention to Keywords: Pay attention to the keywords included in the MCQ questions of Class 6 HCF and LCM so that they can lead to selecting the right options. 
• Eliminate Obvious Wrong Answers: Eliminate those answer options of HCF and LCM MCQ questions for Class 6 which are obviously wrong; this will narrow down the choices to select accurate options. 
• Double Check the Answers: Once students have selected the accurate options of Fraction MCQs, then it is important to double check the given answers so that students can avoid making careless errors. 
• Practise Regularly: To ace in MCQs of Class 6 HCF and LCM, students need to practise sample questions in a proper way so that they don’t make mistakes in the actual exam.
• Seek Help: If students are stuck in solving questions of Class 6 HCF and LCM then they can take the help of their concerned teachers; this can let students score good in it. 

The Ultimate Guide to Solve MCQ Questions for Class 6 ICSE Maths HCF and LCM

If students want to normally solve MCQ questions for Class 6 ICSE Maths HCF and LCM, then they have picked up the wrong approach; this can applicable in solving easy questions but for difficult questions, they need to follow some tips which are discussed below: 

• Manage Time: Students should manage their given time to solve all Class 6 ICSE Maths HCF and LCM MCQ questions so that they don’t miss out on any of the important questions. 
• Use Elimination Method: Elimination generally means to get rid of anything; students need to use this process of eliminating options of MCQ questions of Class 6 HCF and LCM so that they can have more chances of selecting the right option. 
• Read the Given Instruction Properly: The instructions are considered to be an underrated advice but it is quite important to read; before attempting HCF and LCM MCQ questions for Class 6 students need to read the given instructions. 
• Examine Each Option: Before selecting the final response students need to read the options of Class 6 HCF and LCM so that they can select the best option. 
• Stay Focused: While attempting MCQs of Fraction, they need to be very focused and calm so that they can select the accurate options. To stay focused as well as calm while attempting HCF and LCM questions, students can take deep breaths and read the options carefully.
• Answer Easy Questions First: It is advisable for students to answer easy questions of ICSE Class 6 HCF and LCM so that students don’t waste time on tricky questions. Students can identify the easy, moderate, tricky questions of Class 6 HCF and LCM while reading the questions. 

What are the Challenges Faced While Solving MCQ Questions for Class 6 ICSE Maths HCF and LCM?

While solving MCQ questions for Class 6 ICSE Maths HCF and LCM, students may face challenges, but they need to overcome it accordingly; some of the challenges are discussed below: 

• Misunderstanding of Concept: Students need to have a solid understanding of the HCF and LCM concepts; if they don’t have a proper understanding then it is obvious that they may struggle in solving questions. 
• Difficulty in Understanding the Approach: The MCQs of ICSE Class 6 HCF and LCM often require different approaches to solve. So it is possible that students may find it difficult to identify the right approach to solve HCF and LCM questions. 
• Confusions Between Options: If there are similar options of ICSE Class 6 HCF and LCM questions, then students can face difficulty in understanding the differences; so to overcome this they need to analyse the options. 
• Careless Mistakes: Students can make careless mistakes while attempting Class 6 HCF and LCM MCQs such as misreading of questions or options which may lead to selecting the wrong option. 
• Lack of Time Management: The MCQs of HCF and LCM are time bound and students may face difficulty in attempting all questions within the given time limit.
• Tricky Answer Options: The objective questions of HCF and LCM may include tricky options; it is obvious that students may face difficulty in analysing the options and marking the accurate option. 

How to Rectify Mistakes After Solving MCQ Questions for Class 6 ICSE Maths HCF and LCM?

After solving MCQ questions for Class 6 ICSE Maths HCF and LCM, it is important to review the mistakes and rectify them to improve their understanding towards the chapter; below are some steps to rectify: 

• Review Answers: Go through the answers of Class 6 ICSE Maths HCF and LCM MCQ questions; in this students should make sure that they have marked the right option. 
• Identify the Mistakes: Take a note of those HCF and LCM MCQs which you have attempted in a wrong way and analyse the cause of the mistakes. This can help you to focus on those areas of HCF and LCM questions which need improvement. 
• Understand the Correct Answer: Students should understand the correct answers of MCQ questions of Class 6 HCF and LCM; like review the answers and analyse the explanation given so that they can attempt questions in the same approach. 
• Correct Mistakes: This is the important phase while attempting HCF and LCM MCQ questions for Class 6 so that students don’t repeat the same mistakes in the future. 
• Retake The MCQ: It is advisable for students to retake the same set of Class 6 HCF and LCM MCQs in order to rectify the mistakes; through this they can track their performance. 
• Focus on Problem Areas: If students are facing problems in specific types of problems or Class 6 HCF and LCM questions, then it is advisable for them to focus on those to rectify the mistakes. 

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• Mathematics CBSE
• Real Numbers
• The Fundamental Theroem of Arithmetic

11. Case study based question: Prime factors and HCF

Exercise condition:.

• Every composite number can be expressed as a product of prime numbers
• Every prime numbers can be expressed as a product of composite numbers
• Every composite number may or may not be expressed as a product of prime numbers
• Every prime number may or may not be expressed as a product of composite numbers
• Neither prime nor composite
• Composite number
• Square number
• Prime number