Least Common Multiple
The smallest (nonzero) 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 2,3,4,5, etc). Just like the multiplication table.
Here are some examples:
The mutlples of 3 are 6, 9, 12, 15, 18, 21, etc ... 
The mutlples of 12 are 24, 36, 48, 60, 72, etc... 
What is a "Common Multiple" ?
If you have two (or more) numbers, and you check through their multiples and find the same value in both lists then that is a common multiple of those numbers.
For example, if you write down the multiples of two different numbers (say 4 and 5) the common multiples are those that are found in both
numbers:
The multiples of 4 are 8,12,16,20,24,28,32,36,40,44,... 
The multiples of 5 are 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 1: Find the least common multiple for 3 and 5:
The multiples of 3 are 6, 9, 15, ..., and the multiples of 5 are 10, 15, 20, ..., like this: 

As you can see on this number line, the first time the multiples match up is 15. Answer: 15 
And you can find the least common multiple of 3 (or more) numbers.
Example 2: Find the least common multiple for 4, 6, and 8
Multiples of 4 are: 8, 12, 16, 20, 24, 28, 32, 36, ...
Multiples of 6 are: 12, 18, 24, 30, 36, ...
Multiples of 8 are: 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.
