Finding the LCM

Getting Started

Least means the smallest or lowest value. The least common multiple is the smallest multiple a set of numbers have in common. To find the LCM of a set of numbers, you first need to identify the multiples of each number individually.

Consider the numbers 6 and 8.

First, list multiples for each number.

Multiples of 6: 6, 12, 18, 24, 30, 36, 42
Multiples of 8: 8, 16, 24, 32, 40, 48

What do they have in common?

Take note that a list of multiples can go on and on; each number has an infinite number of multiples. You might not need to list too many multiples before you find the LCM. A good way to start off is to list 3 to 5 multiples of each number. Compare them for any common multiples then, if needed, list a few more multiples.

Remember you are looking for the least common multiple, which is the first (smallest) number they have in common. With some numbers, you will find that very quickly and only need to list a few multiples.

Once you have listed a few multiples of each number, compare your lists to see if you have found a common multiple--a multiple that is in both lists.

Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48
Multiples of 8: 8, 16, 24, 32, 40, 48

In the multiple lists, you can see that 6 and 8 have the common multiples of 24 and 48.

Name the LCM

If you keep listing multiples of 6 and 8, you will find other multiples they have in common. Keep in mind that you are looking for the LCM, least common multiple. You only need the first multiple that they share.

The first common multiple that they share is the smallest, or least common multiple (LCM). So, the LCM for 6 and 8 is 24.