problem solving involving gcf and lcm

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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)

Use this worksheet to check your 6th grade students’ understanding of GCF and LCM. 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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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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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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• Sixth Grade lessons
• How to find the GCF and the LCM word problems

" class="arrow-title-img"> How to find the GCF and the LCM word problems

This enriching resource on how to find the GCF and LCM word problems is here to improve your kids' technical skills and performance in solving word problems efficiently.

Also, we will include effective problem-solving and instructional working strategies so that learners can easily tackle word problems concerning GCF and LCM. With this, your kids can wave goodbye to all the substantial challenges they face or encounter in solving math word problems.

In fact, with this resource, kids can easily identify the problem type and translate the problem into a solvable mathematical equation, thereby providing an accurate result for the word problem.

Steps on how to find the GCF and LCM word problems

Your kids will be excited as they discover simple steps on how to find the GCF and LCM word problems . These steps will model and help young learners easily identify the relational statements in any word problem they encounter. We will begin by designing easy rules to find GCF /LCM.

Also, our resource will guide your kids through identifying key problem features in word problems concerning HCF/LCM. And how to transform math problems into meaningful maths equation.

As we know, learning with examples is usually a great lesson for kids. Hence, this resource will present real-life situation examples to demonstrate how these steps work

Step 1: IDENTIFY:

• You have to start by reading the whole word problem very carefully.
• Then, figure out the scenario that the problem needs you to tackle.
• Last but not least, use the keywords found in the word problem to help you identify the operation you are supposed to carry out efficiently.

Speaking of keywords:

• When looking for GCF in a word problem, these are some of the general keywords you'll come across in the word problem: - greatest, largest, maximum, highest, etc.
• Another clue to know if you need to find the GCF in a word problem is when the problem presents itself as "groups," "rows," "sections," "how many sets," "divided into equal groups," "identical" "split," "share equally" "same combination," "same" "even amount," etc.
• When finding the LCM , these are some general keywords that you'll find in the word problem: - least, minimum, smallest, lowest, etc.
• Similarly, other clues to know if you are going to find but the LCM in a word problem is when the problem presents itself as an event that will repeat itself , when you find the word "every…" in the word problem, etc.
• ***One key Element for learners to understand is that they should not always rely on keywords alone . That is to say; the same keyword can have different meanings in different word problems .
• For this reason, we reiterate on the importance of reading the question very carefully to understand the situation that the word problem is describing , then figure out exactly which operation to use***

Step 2: STRATEGIZE:

At this stage, you should ask yourself, "how am I going to solve the problem?"

• You already know that, from the keyword(s) in the word problem, you will know if you need to look for the LCM or GCF .
• However, you don't have to depend entirely on keywords . Always try to understand the situation that the problem is describing very well before you start solving it.
• After knowing which operation you will perform, construct short expressions/sentences representing the given word problem.

Step 3: SET UP:

Now, write down a numerical expression representing the information given in the word problem.

Step 4: PROVIDE A SOLUTION:

From step 3 above,

If the word problem needs you to find the GCF , use any of the methods listed below:

• The factor tree and column method,
• The slide method,
• The prime factor method.

If the word problem needs you to find the LCM , use one of the following methods:

• Listing the multiples method,
• Prime factorization method,
• Division method,
• The factor tree and column method.

Step 5: CHECK YOUR WORK:

Finally, ask yourself this question. "Does my answer make sense?" If "YES," you are done. If "NO," go back to step 1 and start all over again.

You can always do this by solving to prove your answer, as shown in the attached example below.

Find more practices with these tests online

• Greatest common factor word problems
• Lowest common multiple word problems
• number theory

GCF and LCM word problems

Convert between standard and scientic notation

Compare numbers written in scientific notation

Examples on how to solve the GCF and LCM word problems

Example one: how to find the gcf word problem.

Step 1: First, read the problem carefully and identify the keyword(s) found in the word problem. After doing this, you see that the keywords in the problem are "largest" and "each."

Step 2: Next, how will you solve the problem? From the situation the problem describes, the keyword found in the word problem and the clue, which is "must be shared equally," calls for you to look for the GCF .

With this in mind, construct short expressions/sentences to represent the given word problem.

• Number of cans of juice bought= 100
• Number of hamburgers bought = 50
• Number of packets of potato chips = 50
• Therefore, the largest number of students that can go for the field trip for all the food to be shared equally with no leftovers = the GCF of 100 and 50.

Merge Step 3 and 4: when dealing with the GCF, step 3 and 4 are best understood when merged.

• Start by writing down a numerical expression to represent the bolded sentence in step 2 above, then find the GCF of 100 and 50 using the prime factor method.
• Firstly, find the prime factors of each number 50 = 2 × 5 × 5. 100 = 2 × 2 × 5 × 5
• Secondly, find and highlight the prime factors that the factors have in common. 50 = 2 x 5 x 5 . 100 = 2 x 5 x 2 x 5 .
• Finally, to find the GCF, multiply their common factors together. 2 × 5 × 5 = 50

So, 50 students can go for the field trip if all the food must be shared equally with no left over.

GCF of 100 and 50 = 50

• 100 cans of juice ÷ 50 = 2 cans of juice.
• 50 hamburgers ÷ 50 = 1 hamburger
• 50 packets of potato chips ÷ 50 = 1 packet of potato chips

So, each student will get 2 cans of juice, 1 hamburger, and 1 packet of potato chips.

Step 5: Finally, check your work to know if your answer makes sense. You can do this as shown below.

To check if your answer is correct,

Firstly add the number of cans of juice, hamburgers, and packets of potato chips that each student will get = 2 + 1 + 1 = 4

Secondly, add the total number of cans of juice, hamburgers, and packets of potato chips that they bought = 100 + 50 + 50 = 200

Finally, divide the total number of cans of juice, hamburgers, and packets of potato chips by the total number of cans of juice, hamburgers, and packets of potato chips that each student will get = 200 ÷ 4 = 50

So, since the final answer equals the GCF of 100 and 50, it implies that your answer is correct and makes sense.

Example two: how to find the LCM word problem

Step 1: After carefully reading the problem, you see that the keyword in the word problem is "least."

Step 2: Next, how will you solve the problem? As you can see, the problem described and the keyword found in the word problem show that we should find the LCM .

With this in mind, form short expressions/sentences to represent the given word problem.

• Packages of sandwich rolls = 12
• Packages of sausages = 6
• Packages of hamburger buns = 8
• Packages of hamburger meat patties = 6
• Therefore, the least number of people she can serve if she buys the least number of packages of each item = the LCM of 12, 8, and 6.

Merge Step 3 and 4: Fwhen dealing with LCM, step 3 and 4 are best understood when merged.

*Now, write down a numerical expression to represent the bolded sentence in step 2 above and then proceed to find the LCM of 15 and 40 using the listing multiples method.

• Firstly, list and find the multiples of 12, 8, and 6. 12 = 12, 24, 36 … 6 = 6, 12, 24, 30, 36 … 8 = 8, 16, 24, 36 …
• Secondly, find and highlight the common multiples. 12 = 12, 24 , 36 … 6 = 6, 12, 24 , 30, 36 … 8 = 8, 16, 24 , 36 …
• Thirdly, the common multiples of the numbers are 24 , 36 …
• Finally, the least common multiple of the numbers is 24 .

So, she can serve 24 people if she buys the least number of packages of each item.

To check if your answer is correct, divide the least common multiple of 12, 8, and 6 by the number of items they bought, i.e., 4 items.

Result: 24 ÷ 4 = 6

Then if you multiply the result by 4 (the number of items) and it gives you the least multiple of 12, 8, and 6, it implies that your answer is correct.

6 × 4 = 24

So, since the final answer is equal to the LCM of 12, 8, and 6, it implies that your answer is correct and makes sense .

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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.

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• Grade 6 LCM Worksheets
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GCF and LCM Word Problems Worksheets

• Pre-Algebra >
• Factors >
• GCF and LCM Word Problems

Our printable worksheets on GCF and LCM word problems are an effective resource that dramatically improves problem-solving skills. Children are expected to read the scenario carefully and look for keywords that help determine whether they need to find the lowest common multiple or the greatest common factor. Have a blitz on our effective practice resources!

Our pdf LCM and GCD word problems worksheets are ideal for 6th grade and 7th grade children.

Related Printable Worksheets

▶ Greatest Common Factor

▶ Least Common Multiple

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Ordering Rational Numbers

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LCM & GCF Word Problems

Mathematics.

17 questions

Introducing new   Paper mode

No student devices needed.   Know more

• 1. Multiple Choice Edit 30 seconds 1 pt The school cafeteria serves tacos every sixth day and cheeseburgers every eight day. If tacos and cheeseburgers are both on today’s menu, how many days will it be before they are both on the menu again? 14 days 24 days 34 days 44 days
• 2. Multiple Choice Edit 30 seconds 1 pt A radio station is giving away a $100 bill to every 30th caller and movie tickets to every 40th caller.  Which caller will be the first to win both prizes? 5 2 10 120
• 3. Multiple Choice Edit 30 seconds 1 pt Two clocks are turned on at the same time. One clock chimes every 15 minutes. The other clock chimes every 25 minutes. In how many minutes will they chime together? 55 minutes 25 minutes 60 minutes 75 minutes
• 4. Multiple Choice Edit 30 seconds 1 pt Henry and Margo both began traveling around a circular track. Henry is riding his bike, and Margo is walking. It takes Henry 7 minutes to make it all the way around, and Margo takes 12 minutes. How much time will pass until they meet at the starting line? 84 minutes 48 minutes 854 minutes 78 minutes
• 5. Multiple Choice Edit 30 seconds 1 pt Jenny goes to  karate class every 12 days.and too the library every 18 days. On December 1st she went to both class and the library. On what date will she do both class and go to the library? 24 days 36 days 42 days 52 days
• 6. Multiple Choice Edit 30 seconds 1 pt Melanie and Martin are both building a toy train track out of connecting pieces. Melanie has pieces that are 8 inches long while Martin's pieces are 20 inches long.  How long will the shortest track be that they can each build with the same length? 2 40 4 20
• 9. Multiple Choice Edit 30 seconds 1 pt Lisa is making activity baskets to donate to charity.  She has 12 coloring books, 28 markers, and 36 crayons.  What is the greatest number of baskets she can make if each type of toy is equally distributed among the baskets? Greatest Common Factor Least Common Multiple
• 10. Multiple Choice Edit 30 seconds 1 pt At Kentucky Fried Chicken, the kitchen staff baked 96 chicken legs, 144 thighs, and 224 wings. The staff had to prepare platters for a catered lunch at an office. Each platter will have the same number of legs, thighs, and wings. How many platters can the staff make if they want the greatest number of chicken pieces on each platter? Greatest Common Factor Least Common Multiple

At the movie theater, they give out a free drink to every 5th customer and a free bag of popcorn to every 3rd customer. Who is the first customer that is going to win both free items?

16th customer

15th customer

3rd customer

1st customer

• 12. Multiple Choice Edit 5 minutes 1 pt Lincoln Vitamin Shop sold equal quantities of Vitamin A and Vitamin D supplements this morning, even though the Vitamin A supplements come in packs of 4 and the Vitamin D supplements in packs of 15. What is the smallest number of each type that the store could have sold? 15 45 60 30
• 13. Multiple Choice Edit 5 minutes 1 pt Cups are sold 5 to a package and plates are sold 10 to a package. If you want to have the same number of each item for a party, what is the least number of packages of each you need to buy? 30 20 50 10
• 14. Multiple Choice Edit 3 minutes 1 pt Jane has 18 juice boxes, 24 bags of peanuts and 36 apples.  She wants to make snack bags with the same number of each thing in each bag.  What is the greatest number of snack bags Jane can make. 4 6 8 10
• 15. Multiple Choice Edit 30 seconds 1 pt Maya had 16 red flowers and 24 yellow flowers.  She wants to make bouquets with the same number of each color flower in each bouquet.  What is the greatest number of bouquets that she can make? 4 2 48 8

Miss Friedman is planning a surprise birthday party for Miss Pabon. Miss Friedman is trying to make party favors for all her guests and wants no left overs. She has 18 party hats and 24 noise makers. How many party favors can she make?

6 party favors with 18 hats and 24 noise makers

6 party favors with 3 hats and 4 noise makers

6 party favors with 2 hats and 2 noise makers

24 party favors with 18 hats and 18 noise makers

• 17. Multiple Choice Edit 5 minutes 12 pts Which is a NOT a factor of 9? 0 1 3 9

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