Least Common Multiple Worksheets

Become A Pro At Finding The LCM Of 2 Or More Numbers Using These Least Common Multiple Worksheets

By the time kids start grade 5, they start learning more advanced topics of arithmetic. One of these topics is the Least Common Multiple or LCM. The Least Common Multiple (LCM) is also known as the Lowest Common Multiple (LCM) or Smallest Common Multiple (SCM). 

In arithmetic, the multiple of any given number is a number, which can be divided by the given number without leaving a remainder. 

For example: Let’s say 10 is a multiple of 2.

5 x 2 = 10 and,

10 ÷ 5 = 2.

The Least Common Multiple of 2 or more numbers is the smallest common number, which is a multiple of both numbers. 

For example: Let’s consider the numbers 3 and 5. They each have their own set of multiples.

Multiples of 3: 3, 9, 12, 15, 18, 21, 24, 27, 30…

Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50…

Circle the common multiples of 3 and 5.

Circle the common multiples of 3 and 5: Least common multiple worksheets

The common multiples of 3 and 5 are 15 and 30.

To find the least common multiple of 3 and 5, let’s draw a number line from 1 – 20. Then, circle the least common multiple of 3 and 5 on the number line.

Find the common multiples using number line: Free printable least common multiple worksheets

So, the least common multiple (LCM) of 3 and 5 is 15.

Least Common Multiple Worksheets

The best way to learn how to determine the LCM for 2 or more numbers is to practice. These Least Common Multiple worksheets are a great way to learn how to find the LCM for any given number. Practice solving LCM problems on these Least Common Multiple worksheets:

Least Common Multiple Worksheets: Multiples Method

Find the LCM for the numbers in the worksheet using the multiples method. List all the multiples of the numbers to find the least common multiple of the given numbers.

Find the common multiples from the given numbers: Free least common multiples worksheets

Least Common Multiple Worksheets: Find The LCM Using The Prime Factorization Method:

Find the LCM:  Least common multiple printable worksheets for kids

Least Common Multiple Worksheets using Division Method

Find the LCM for the given numbers in the worksheet using the division method or the grid or ladder method.

Find the LCM using division method:  Least common multiple worksheets for kids

Least Common Multiple Worksheets: Find The LCM For 3 Numbers

Trace the LCM among the numbers: Worksheet on least common multiples

How to find the Least Common Multiple (LCM) between 2 or more numbers

There are several different ways to determine the least common multiple (LCM) of 2 or more numbers.

  1. The prime factorization method
  2. The repeated division method
  3. The multiples method

Using prime factorization to find the LCM

To find the least common multiple for 2 or more numbers using this method, write down the numbers at the top. Now, create a factorization tree with the multiples of both the numbers. The least prime factors for the numbers are in the last branch of the factorization tree.

For example: Let’s create a factorization tree for the numbers 28 and 72.

Then, list common multiples and the remaining multiples of both the numbers. 

28 = 2 x 2 x 7 = 22x 32

72 = 2 x 2 x 2 x 3 x 3 = 23x 32x 7

Now, multiply all the prime factors with the highest degree to get the LCM. This means that you have to multiply each factor the greatest number of times it appears in either of the numbers.

For example: The factor 2 appears twice under 28 and it appears thrice under 72. The factor 3 appears twice under 72. And, 7 appears only once under 72. So, the equation is:

LCM of 28 and 72 = 23x 32x 7 = 2 x 2 x 2 x 3 x 3 x 7 = 504.

Therefore, the least common multiple (LCM) of 28 and 72 is 504.

How to find the LCM using the repeated division method

To obtain the LCM using this method, the given numbers are divided by common divisors until they cannot be divided any further. The product from multiplying the common divisors and the remainders is the Least Common Multiple of the given numbers. Here is an example.

Let’s find the LCM for 48 and 60.

248,60
224,30
312,15
4,5

Multiply the common divisors and the remainders.

So, 2 x 2 x 3 x 4 x 5 = 240

Therefore, the Least Common Multiple (LCM) of 48 and 60 is 240.

This method of finding the Least Common Multiple is also called the grid or ladder method.

Let’s try another example. Let’s find the LCM for 24, 36 and 66.

224,36,66
212,18,33
36,9,33
2,3,11

Now, multiply the common divisors and the remainders.

So, 2 x 2 x 3 x 2 x 3 x 11 = 792.

Therefore, the Least Common Multiple (LCM) of 24, 36 and 66 is 792.

Finding LCM using the multiples method 

To determine the LCM of the given numbers using this method, list all the multiples of both the numbers. The first common multiple for both numbers is the least common multiple for those numbers. Here is an example.

Let’s find the LCM for 10 and 15 using the multiples method. 

List the multiples of both the numbers.

Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100…

Multiples of 15: 15, 30, 45, 60, 75, 80, 105, 120, 135, 150…

Underline the common multiples of 10 and 15.

Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100…

Multiples of 15: 15, 30, 45, 60, 75, 80, 105, 120, 135, 150…

The common multiples of 10 and 15 are 30 and 60. The first common multiple for both numbers is 30. 

Therefore, the LCM of 10 and 15 = 30

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Frequently Asked Questions on Least Common Multiple Worksheets

What are the examples of Least Common Multiple of 5?

The examples of Least Common Multiple of 5 are 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75.

What are the types of Least Common Multiple Worksheets?

The different types of Least Common Multiple Worksheets are Least Common Multiple Worksheets: multiples method, Least Common Multiple Worksheets: division method, and Least Common Multiple Worksheets: Find The LCM Using The Prime Factorization Method.