problem solving involving gcf and lcm grade 4

Word Problems that uses GCF or LCM (Worksheets)

Related Topics & Worksheets: Least Common Multiple More Math Worksheets

Objective: I can find the least common multiple or least common denominator.

Read the lesson on least common multiple if you need to learn how to find the lowest common multiple.

We use the least common multiple when adding or subtracting fractions with unlike denominators. It is then called the least common denominator.

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Gcf and Lcm Word Problems Worksheets

GCF and LCM word problems worksheets can help encourage students to read and think about the questions, rather than simply recognizing a pattern to the solutions. GCF and LCM word problems worksheets come with the answer key and detailed solutions which the students can refer to anytime.

Benefits of GCF and LCM Word Problems Worksheets

GCF and LCM word problems worksheets help kids to improve their speed, accuracy, logical and reasoning skills.

GCF and LCM word problems worksheets give students the opportunity to solve a wide variety of problems helping them to build a robust mathematical foundation. GCF and LCM word problems worksheets help kids to improve their speed, accuracy, logical and reasoning skills in performing simple calculations related to the topic of GCF and LCM.

GCF and LCM word problems worksheets are also helpful for students to prepare for various competitive exams.

These worksheets come with visual simulation for students to see the problems in action, and provides a detailed step-by-step solution for students to understand the process better, and a worksheet properly explained about the GCF and LCM.

Download GCF and LCM Word Problems Worksheet PDFs

These math worksheets should be practiced regularly and are free to download in PDF formats.

☛ Check Grade wise GCF and LCM Worksheets

• Grade 6 LCM Worksheets
• 6th Grade GCF Worksheets

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GCF and LCM

Here you will learn about GCF and LCM (greatest common factor and least common multiple), including how to find the GCF and LCM of two or more numbers using the prime factorization method and recognize when to find the GCF or the LCM in word problems.

Students will first learn about GCF and LCM as part of the number system in 6th grade.

What is GCF and LCM?

GCF and LCM are two abbreviations for the greatest common factor (GCF) and the least common multiple (LCM).

The greatest common factor (GCF) is the largest whole number that two or more numbers can be divided by. The lowest common multiple (LCM) is the smallest whole number which is a multiple of two or more whole numbers.

Let’s take a look at some examples below:

• Example of GCF , also known as the greatest common divisor (GCD) and the highest common factor (HCF). Find the GCF of 8 and 12. Let’s start by writing the factors of 8 and 12. Factors of {\bf{8}} {\textbf{: }} 1, 2, 4, 8 Factors of {\bf{12}} {\textbf{: }} 1, 2, 3, 4, 6, 12 There are several numbers that occur in both lists ( 1, 2, and 4 ). The largest factor that occurs in each list is 4, and so the greatest common factor of 8 and 12 is \bf{4}.
• Example of LCM Find the LCM of 8 and 12. Let’s start by writing the first 12 multiples of 8 and 12. Multiples of {\bf{8}} {\textbf{: }} 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96 Multiples of {\bf{12}} {\textbf{: }} 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144 There are several values that occur in both lists ( 24, 48, 72, and 96 ). The lowest of these is 24, hence the least common multiple of 8 and 12 is \bf{24}.

Prime factor decomposition

To calculate the GCF or LCM of two or more numbers, you can write out a list of factors or multiples as we have above, however, this approach can be very time consuming and can be complicated when dealing with factors and multiples of large numbers ( 3 digit numbers in particular).

You can therefore use prime factorization to find these values.

The fundamental theorem of arithmetic states that every positive whole number greater than one is either a prime number, or can be written as a product of its prime factors. Every number has a unique set of numbers called prime factors.

By presenting prime factors within a Venn diagram , you can quickly determine both the GCF and LCM of the two or more numbers in the question.

For example,

8=2\times{2}\times{2}

12=2\times{2}\times{3}

The intersection of the two circles contains the greatest common factor , where you multiply the values within the intersection together .

Here, the GCF of 8 and 12 is equal to 2\times{2}=4.

The union of the two circles contains the least common multiple where you multiply the values within both circles together .

Here, the LCM of 8 and 12 is equal to 2\times(2\times{2})\times{3}=24.

As the least common multiple is found by multiplying all of the factors together within the Venn diagram, the least common multiple can be found by multiplying the greatest common factor by the remaining prime factors.

This allows you to solve problems where you are given the GCF and LCM of two numbers and you need to determine the original two numbers.

Common Core State Standards

How does this relate to 6th grade math?

• Grade 6 – The Number System (6.NS.4) Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers (1–100) with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 \, as \, 4 (9 + 2).

[FREE] GCF and LCM Worksheet (Grade 6 to 8)

Use this worksheet to check your grade 6 to 8 students’ understanding of the greatest common factors and lowest common multiples of numbers. 15 questions with answers to identify areas of strength and support!

How to find the greatest common factor

In order to find the greatest common factor of two or more numbers:

State the product of prime factors for each number.

Write all the prime factors for each number into a Venn diagram.

Multiply the prime factors in the intersection to find the GCF.

How to find the least common multiple

In order to find the least common multiple of two or more numbers:

Multiply each prime factor in the Venn diagram to find the LCM.

GCF and LCM examples

Example 1: gcf of two simple composite numbers.

Find the greatest common factor of 30 and 42.

2 Write all the prime factors for each number into a Venn diagram.

3 Multiply the prime factors in the intersection to find the GCF.

GCF =2\times{3}=6.

Example 2: LCM of two simple composite numbers

Calculate the least common multiple of 16 and 18.

16=2\times{2}\times{2}\times{2}

18=2\times{3}\times{3}

LCM =(2\times{2}\times{2})\times{2}\times(3\times{3})=8\times{2}\times{9}=144.

Example 3: GCF word problem

120 \ ml of red paint and 156 \ ml of blue paint are mixed together to create a tin of purple paint. The paint is then distributed equally into sample tubes. Each tube must contain the same amount of paint that must be over 20 \ ml.

What is the maximum number of tubes that can be filled with the minimum amount of paint?

120=2\times{2}\times{2}\times{3}\times{5}

156=2\times{2}\times{3}\times{13}

GCF =2\times{2}\times{3}=12.

The total amount of paint is 120 + 156 = 276 \ ml.

Dividing 276 \ ml into 12 equal shares (the GCF), we have

276\div{12}=23.

As each tube must contain over 20 \ ml of paint, we must have 12 tubes, each containing 23 \ ml of paint.

Example 4: LCM word problem

A plumber is fixing multiple leaking pipes. Pipe A drips water every 12 seconds. Pipe B drips water every 22 seconds. Both pipes drip at the same time. How much time passes before they next drip at the same time? Write your answer using minutes and seconds.

22=2\times{11}

LCM =(2\times{3})\times{2}\times{11}=6\times{2}\times{11}=132

132 seconds pass. Converting this to minutes and seconds is 2 minutes and 12 seconds ( 60 + 60 + 12 = 132 , with 60 seconds = 1 minute).

How to find the original values given the GCF and the LCM

In order to find the original values given the GCF and the LCM:

• Divide the LCM by the GCF.

Calculate the product of primes of the remainder.

Determine which prime factors match each original number.

Example 5: find the numbers, given the GCF

The greatest common factor of 3 numbers is 7. The product of their remaining prime factors is 30 and each number is greater than 10. Determine the value of the three numbers.

Divide the LCM by the GCF to determine the remainder.

As we already know the remainder ( 30 ), we can move on to step 2.

Using a prime factor tree, the product of primes for 30 is:

30=2\times{3}\times{5}

As each value is greater than 10, the GCF 7 must be a factor of all 3 numbers and it must be multiplied by another factor. 30 has 3 prime factors, 2, 3, and 5 and so the original three numbers are:

A=7\times{2}=14

B=7\times{3}=21

C=7\times{5}=35

Example 6: find the original numbers given the GCF and LCM

Two numbers, A and B, have the following number properties:

• GCF (A,B) = 7
• LCM (A,B) = 2,310
• A is divisible by 3
• B is an even number
• 100<A<B

Determine the values of A and B.

2310\div{7}=330

Using a prime factor tree, the product of primes for 330 is:

330=2\times{3}\times{5}\times{11}

As A is divisible by 3, two factors of A must be 3 and 7 (the GCF).

As B is even, two factors of B must be 2 and 7 (the GCF).

Writing this up so far, we have

A=3\times{7}\times{x}

B=2\times{7}\times{y}

As 330=2\times{3}\times{5}\times{11}, we have the remaining factors of 5 and 11 to place.

As 100<A<B, both A and B are greater than 100 with A being smaller than B. The only way this is possible is by making x=5 and y=11.

This means that,

A=3\times{7}\times{5}=105

B=2\times{7}\times{11}=154

The solution is A = 105 and B = 154.

Tips for teaching GCF and LCM

• Before introducing GCF and LCM, students should have a strong understanding of factors and multiples, which they would have first learned in 4th grade. Review these terms and practice listing factors and multiples if needed.

Easy mistakes to make

• Finding the GCF instead of the LCM (and vice versa) A very common misconception is mixing up the greatest common factor with the least common multiple. Factors are composite numbers that are split into smaller factors. Multiples are composite numbers that are multiplied to make larger numbers.
• Incorrect evaluation of powers It is possible to write prime factors into a Venn diagram with their associated exponent or power. This only becomes an issue when the powers are not correctly interpreted. We suggest having students write the prime factors without the use of exponents. Take, for example, the numbers 12 and 18. 12=2^{2}\times{3} 18=2\times{3}^{2} Here, 2^{2}=2\times{2}=4 which is correct, however, the same misconception could then be continued to 3^{2}=3\times{2}=6, which is incorrect. Instead, 3^{2}=3\times{3}=9. This will have an impact on the value of the GCF and the LCM.

Related lessons on factors and multiples

• Factors and multiples
• Factor tree
• Least common multiple
• Greatest common factor
• Prime factors
• Factor pairs

Practice GCF and LCM questions

1. Find the GCF of 54 and 60.

GCF (54,60) = 2\times{3}=6

2. Find the LCM of 24 and 32.

LCM (24,32) = 3\times(2\times{2}\times{2})\times(2\times{2})=3\times{8}\times{4}=96

3. Two lengths of ribbon measure 1.2 \ m and 80 \ cm. Each piece of ribbon needs to be cut into the fewest number of pieces of the same length. What is the length of each piece?

GCF (80,120) = 2\times{2}\times{2}\times{5}=40

4. Two runners leave the start line of a 200 \ m track on the whistle. It takes runner A \ 1 minute to run 1 lap of the track and runner B \ 1 minute and 12 seconds. What distance will runner B have traveled when they next cross the start line at the same time?

Converting both lap times to seconds, runner A takes 60 seconds, and runner B takes 72 seconds.

GCF (60,72)=2\times{2}\times{3}=12

LCM (60,72) = 5 \times 12 \times (2 \times 3)=5 \times 12 \times 6=360

360 seconds = 6 minutes

6\div{1.2}=5 laps

5. The greatest common factor of two numbers is 35. The product of the remaining factors is 33. Both original numbers contain three digits. What is the difference between the two original numbers?

Smaller number: 35\times{3}=105

Larger number: 35\times{11}=385

6. Two numbers x and y have the following number properties:

• \text{LCM }(x,y)=96
• \text{GCF }(x,y)=8
• 2<x<y<40

What is the value of x+y?

GCF and LCM questions

1. A farm needs to divide their two fields into equal-sized enclosures for some horses. Field 1 is 240 \ m^2. Field 2 is 160 \ m^2. Each horse must have at least 42 \ m^2.

(a) What is the minimum possible area for each enclosure?

(b) What is the maximum number of horses that can use these two fields?

240=2^4 \times 3 \times 5 \, or \, 240=2 \times 2 \times 2 \times 2 \times 3 \times 5

160=2^5 \times 5 \, or \, 160=2 \times 2 \times 2 \times 2 \times 2 \times 5

GCF (240,160)=80 \ m^2

2+3=5 \, or \, (240+160) \div 80=5

2. Given that 6480=2^4 \times 3^4 \times 5, simplify the ratio 10800:6480.

GCF (10800,6480)=2^4 \times 3^3 \times 5

Remaining factors are 5 (for 10800 ) and 3 (for 6480 ).

3. The least common multiple of x and y is 2^3 \times 3^2 \times 5^2 where x is a square number such that 36<x<225.

(a) Find the exact value of x.

(b) The greatest common factor of x and y is 4. Determine the value of y. Use the Venn diagram below to help you.

x=2^2 \times 5^2 or

GCF and LCM FAQs

Step 1: State the product of prime factors for each number. Step 2: Write all the prime factors for each number into a Venn diagram. Step 3: Multiply the prime factors in the intersection to find the GCF.

Step 1: State the product of prime factors for each number. Step 2: Write all the prime factors for each number into a Venn diagram. Step 3: Multiply each prime factor in the Venn diagram to find the LCM.

To find the GCF, list all prime factors that are common between the two numbers and multiply them together. To find the LCM, multiply the GCF by all the prime factors of both numbers that have not yet been used.

The least common denominator (LCD) is the least common multiple (LCM) of the denominators of two or more fractions.

The next lessons are

• Converting fractions, decimals, and percentages
• Fractions operations

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GCF and LCM word problems

Factors and multiples.

These word problems need the use of greatest common factors (GCFs) or least common multiples (LCMs) to solve. Mixing GCF and LCM word problems encourages students to read and think about the questions, rather than simply recognizing a pattern to the solutions.

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Calcworkshop

GCF and LCM Explained w/ 7 Step-by-Step Examples!

// Last Updated: November 9, 2020 - Watch Video //

Do you ever get GCF and LCM confused?

Jenn, Founder Calcworkshop ® , 15+ Years Experience (Licensed & Certified Teacher)

It happens, right?

Well, today, we’re going to learn the one method that gets you the answers to both very easily.

Let’s go!

But first let’s review the basic definitions of each.

What Is GCF And LCM

The Greatest Common Factor (also known as GCF ) is the largest number that divides evenly into each number in a given set of numbers.

The Least Common Multiple (also known as LCM ) is the smallest positive multiple that is common to two or more numbers.

Why Do You Need Both Methods

So will there ever be a time when we will need to use both the GCF, Greatest Common Factor and LCM, Least Common Multiple?

Yes, whenever we perform operations with fractions !

For instance, we may need to use the LCM to help us add two fractions , and also the GCF to simplify our result .

Consequently, you will need to know how to use both of these techniques at the same time.

How To Find GCF And LCM

How do you keep them straight and not mix them up?

Great question!

First, whenever you are asked to find both the greatest common factor and the least common multiple, always choose the prime factorization method , or the listing of prime factors, as it will save you time and is the only method that will work consistently.

And secondly, use the last letters of GCF and LCM to find what you need!

Here’s a trick: GC F = F ewer and LC M = More

Remember, when using our prime factorization technique , we choose the fewest common factors for the GCF, and for the LCM, we choose the most of each factor as discussed at Minnesota State University .

Example #1 — Two Numbers

Working a few problems will help to make sense of how this works.

For our first question, let’s find the GCF and find the LCM of two numbers: 12 and 18

Find GCF and LCM of Two Numbers — Example

This means that the GCF of (12 and 18) is 6, and the LCM of (12 and 18) is 36.

Example #2 — Three Numbers

Now let’s work a problem involving three numbers.

Find the GCF and LCM of 15, 18, 24

Find GCF and LCM of Three Numbers — Example

• The GCF of (15, 18, and 24) is 3.
• And the LCM of (15, 18, and 24) is 360.

Using prime factorization and our trick for remembering what factors to choose is a snap!

Closing Thoughts

Now, I would like to point out that the phrase GCF has many synonyms. So, if you ever hear or see one of these alternate phrases, don’t be alarmed. Just know they all mean the same thing – find the greatest positive integer that divides evenly into two or more numbers.

The alternative terminologies for the Greatest Common Factor (GCF) are:

• Highest Common Factor (HCF)
• Greatest Common Divisor (GCD)
• Greatest Common Measure (GCM)
• Highest Common Divisor (HCD)

And while there are no alternate terminologies for Least Common Multiple, you will hear Least Common Multiple (LCM) and Least Common Divisor (LCD) used together quite often. Sometimes, they will be used interchangeably .

The LCM is how we find common multiples of two or more numbers, whereas the LCD is the least common multiple in a fraction’s denominator. So, the LCD is a subset or special case of the LCM. But in all honesty, they require the same math process, so many teachers and students use these two phrases as synonyms.

But, regardless of what the technique is called, the process for finding the greatest common factor and the least common multiple is very straightforward.

Worksheet (PDF) — Hands on Practice

Put that pencil to paper in these easy to follow worksheets — expand your knowledge!

GCF and LCM — Practice Problems GCF and LCM — Step-by-Step Solutions

Video Tutorial — Full Lesson w/ Detailed Examples

Together we will work through various exercises involving two and three numbers to master the techniques of finding the GCF and LCM and never getting them mixed up.

• Introduction to Video: GCF and LCM
• 00:00:26 – How do you find the Greatest Common Factor and the Least Common Multiple?
• 00:01:45 – Find both the GCF and LCM (Examples #1-3)
• 00:14:17 – Determine the GCF and the LCM of three numbers (Examples #4-7)
• Practice Problems with Step-by-Step Solutions
• Chapter Tests with Video Solutions

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Solving Real-life Problems Involving GCF...

Mathematics.

Solving Real-life Problems Involving GCF and LCM of 2 Given

10 questions

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There are 28 white balls and 35 green balls. If the balls will be placed in boxes with the same number, what is the biggest number of balls in a box?

What is asked in the problem?

The smallest number of balls in a box.

The greatest number of balls in a box.

The least number of green balls in a box.

The greatest number of white balls in a box.

What are the given facts in the problem?

28 white balls and 35 green balls

35 white balls and 28 green balls

48 white balls and 25 green balls

38 white balls and 35 green balls

How will you solve the problem?

By finding the Least Common Factor

By finding the Greatest Common Factor

By finding the Least Common Multiple

By finding the factors

What is the answer to the problem?

The least number of balls in a box is 7.

The greatest number of green balls in a box is 7.

The greatest number of balls in a box is 7.

The least number of white balls in a box is 5.

Problem for 5-7.

Melinda is going to prepare bouquets of 5 roses and 6 daisies. What will be the smallest number of roses and daisies that she will need for her bouquets?

What are the given facts?

bouquets of 6 roses and 6 daisies

bouquets of 6 roses and 5 daisies

bouquets of 5 roses and 6 daisies

bouquets of 5 roses and 5 daisies

Melinda is going to prepare bouquets of 5 roses and 6 daisies. What will be the smallest number of roses and daisies that she will need for her bouquets

By finding the Greatest Multiple

By finding the factors.

A. The smallest number of roses and daisies is 30.

The number or roses and daisies is 20.

The greatest number of daisies is 30.

The number of roses is 36.

Problem for 8-10.

Antonia prepared cassava cakes. She wants to pack them in boxes of 6 and 8 pieces. What is the smallest number of pieces of cassava cake that she can pack using the boxes?

The smallest number of rice cakes that can be pack in boxes.

The greatest number of cassava cakes.

The greatest number of boxes that can be used.

The smallest number of cassava cakes that she can pack using boxes.

By finding the numbers.

By finding the Least Common Multiple.

By finding the Greatest Common Factor.

The smallest number of cassava cakes that she can pack using boxes is 42.

The smallest number of cassava cakes that she can pack using boxes is 48.

The smallest number of cassava cakes that she can pack using boxes is 36.

The smallest number of cassava cakes that she can pack using boxes is 54.

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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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Lcm And Hcf For Grade 4

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