The multiples of 3 are 3, 6, 9, 12, 15, 18, ... etcThe multiples of 5 are 5, 10, 15, 20, 25, ... etc

Find the first Common (same) value: The Least Common Multipleof 3 and 5 is 15

(15 is a multiple of both 3 and 5, and is the smallest number like that.)

## So ... what is a "Multiple" ?

We get a multiple of a number when we multiply it by another number. Such as multiplying by 1, 2, 3, 4, 5, etc, but not zero. Just like the multiplication table. Here are some examples:

 The multiples of 4 are: 4,8,12,16,20,24,28,32,36,40,44,...You are watching: The least common multiple of 3 and 5 The multiples of 5 are: 5,10,15,20,25,30,35,40,45,50,...

## What is a "Common Multiple" ?

Say we have listed the first few 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

List the multiples of the numbers until we get our first match.

### Example: Find the least common multiple of 4 and 10:

The multiples of 4 are: 4, 8, 12, 16, 20, ...and the multiples of 10 are: 10, 20, ...

Aha! there is a match at 20. It looks like this: So the least common multiple of 4 and 10 is 20

### Example: Find the least common multiple of 6 and 15:

The multiples of 6 are: 6, 12, 18, 24, 30, ...and the multiples of 15 are: 15, 30, ...

There is a match at 30

So the least common multiple of 6 and 15 is 30

### Example: Find the least common multiple of 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, ....

See more: The Difference Between Galvanic And Voltaic Cell S, Electrochemistry

So 24 is the least common multiple (I can"t find a smaller one!)

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

## Least Common Multiple Tool

There is another method: the Least Common Multiple Tool does it automatically. (Yes, we waited until the end to tell you!)

Introduction to Fractions Simplifying Fractions Comparing Fractions Least Common Multiple Tool Least Common Denominator Greatest Common Factor Adding Fractions Subtracting Fractions Fractions Index