How to Find Least Common Multiple? (+FREE Worksheet!)

The Least Common Multiple (LCM) of a set of numbers is the smallest positive number that is a multiple of all the numbers in the set. Here, we teach you how to find the Least Common Multiple of two or more numbers in a few easy steps.

Related Topics

• How to Find the Greatest Common Factor (GCF)
• How to Factor Numbers
• How to Order Integers and Numbers

Step by step guide to finding the Least Common Multiple

Two ways to find the Least Common Multiple are:

1- Using the multiplication to find the Least Common Multiple (LCM)

• Step 1: To find the Least Common Multiple of a set of numbers, write each of the numbers in that set along with a list of the first multiples.
• Step 2: The Least Common Multiple is the first number in all lists.

Note: When looking for the Least Common Multiple of two numbers, start by writing a list of multiples of the larger number, but stop writing this list when the number of multiples you have written is equal to a smaller number. Then start writing a list of smaller multiples until one of them matches the second list.

This method works well, especially when you want to find The Least Common Multiple between two numbers, but it may take longer if you have more numbers.

2- Use the prime factors to find the Least Common Multiple (LCM)

• Step 1: List the prime factors of each number.
• Step 2: In each list, underline the items that are most duplicated.
• Step 3: Multiply all the numbers you’ve underlined. The answer is the Least Common Multiple.

Least Common Multiple – Example 1:

Find the LCM for \(8\) and \(6\).

Solution:

Multiples of \(8\): \(8, 16, 24, 32, 40, …\)
Multiples of \(6\): \(6, 12, 18, 24, 30, …\)
LCM \(=24\)

Least Common Multiple – Example 2:

Find the LCM for \(4\) and \(12\).

Solution:

Multiples of \(4\): \(4, 8, 12, 16, 20, …\)
Multiples of \(12\): \(12, 24, 36, 48, 60, …\)
LCM \(=12\)

Least Common Multiple – Example 3:

Find the LCM for \(3\) and \(4\).

Solution:

Multiples of \(3\): \(3, 6, 9, 12, 15, 18, …\)
Multiples of \(4\): \(4, 8, 12, 16, 20, 24, …\)
LCM \(=12\)

Least Common Multiple – Example 4:

Find the LCM for \(9\) and \(12\).

Solution:

Multiples of \(9\): \(9, 18, 27, 36, 45, …\)
Multiples of \(12\): \(12, 24, 36, 48, 60, …\)
LCM \(=36\)

Exercises for Finding Least Common Multiple

Find the LCM for each number pair.

• \(\color{blue}{4,14}\)
• \(\color{blue}{5,15}\)
• \(\color{blue}{16,10}\)
• \(\color{blue}{4,34}\)
• \(\color{blue}{8,3}\)
• \(\color{blue}{12,24}\)

Download Least Common Multiple Worksheet

Answers

• \(\color{blue}{28}\)
• \(\color{blue}{15}\)
• \(\color{blue}{80}\)
• \(\color{blue}{68}\)
• \(\color{blue}{24}\)
• \(\color{blue}{24}\)