Lowest Common Multiple

The multiples of a number are all the numbers that are products of the number and any other integer.

For example:

the multiples of 2 are:

2 × 1, 2 × 2, 2 × 3, 2 × 4, 2 × 5, 2 × 6

which are 2, 4, 6, 8, 10, 12, 14, 16, and so on.

The multiples of 4 are:

4 × 1, 4 × 2, 4 × 3, 4 × 4, 4 × 5, 4 × 6 …..

which are  4, 8, 12, 16, 20, 24, …. etc

What is the Lowest Common Multiple?

The Lowest Common Multiple (LCM) of two or more numbers is the lowest multiple they have in common.

For example the common multiples of 2 and 3.

2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22

3, 6, 9, 12, 15, 18, 21, 24

Common multiples are 6, 12, 18 …

The smallest or lowest of these multiples is 6. 

This means 6 is the LCM 

Worked Example 5.2.1:

Find the first three common multiples of 2, 3 and 4. What is their LCM? 

Solution 

There are two common methods for solving LCM. 

1. Listing method 
2. Product of their prime number  

Method 1 – Listing Method:

The multiples of 2, 3 and 4 

2 = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36

3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45

4 = 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52