Least Common Multiple

The smallest (non-zero) number that is a multiple of two or more numbers.

Least Common Multiple is made up of the words Least, Common and Multiple:

What is a "Multiple" ?

The multiples of a number are what you get when you multiply it by other numbers (such as if you multiply it by 1,2,3,4,5, etc). Just like the multiplication table.

Here are some examples:

The multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, etc ...
The multiples of 12 are: 12, 24, 36, 48, 60, 72, etc...

What is a "Common Multiple" ?

When you list the multiples of two (or more) numbers, and find the same value in both lists, then that is a common multiple of those numbers.

For example, when you write down the multiples of 4 and 5, the common multiples are those that are found in both lists:

The multiples of 4 are: 4,8,12,16,20,24,28,32,36,40,44,...
The multiples of 5 are: 5,10,15,20,25,30,35,40,45,50,...

Notice that 20 and 40 appear in both lists?
So, the common multiples of 4 and 5 are: 20, 40, (and 60, 80, etc ..., too)

What is the "Least Common Multiple" ?

It is simply the smallest of the common multiples.

In our previous example, the smallest of the common multiples is 20 ...

... so the Least Common Multiple of 4 and 5 is 20.

Finding the Least Common Multiple

It is a really easy thing to do. Just start listing the multiples of the numbers until you get a match.

Example: Find the least common multiple for 3 and 5:

The multiples of 3 are 3, 6, 9, 12, 15, ...,
and the multiples of 5 are 5, 10, 15, 20, ..., like this:

multiples

As you can see on this number line, the first time the multiples match up is 15. Answer: 15

More than 2 Numbers

You can also find the least common multiple of 3 (or more) numbers.

Example: Find the least common multiple for 4, 6, and 8

Multiples of 4 are: 4, 8, 12, 16, 20, 24, 28, 32, 36, ...
Multiples of 6 are: 6, 12, 18, 24, 30, 36, ...
Multiples of 8 are: 8, 16, 24, 32, 40, ....

So, 24 is the least common multiple (I can't find a smaller one !)

Hint: You can have smaller lists for the bigger numbers.

Least Common Multiple Tool

There is a another method, you can use our Least Common Multiple Tool to find it automatically.

 

 
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