# 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

**, like this:**

*5, 10, 15, 20, ...*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, So, |

*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.