The multiples the 3 space 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 typical Multipleof 3 and also 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 obtain a multiple that a number when we multiply the by an additional number. Such together multiplying through 1, 2, 3, 4, 5, etc, however not zero. Just like the multiplication table. Here room some examples:

 The multiples of 4 are: 4,8,12,16,20,24,28,32,36,40,44,...You are watching: What is 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 detailed the first couple of multiples the 4 and also 5: the common multiples space those the are found in both lists:

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

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

## What is the "Least usual Multiple" ?

It is merely the smallest that the typical multiples.

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

... Therefore the Least common Multiple that 4 and 5 is 20.

## recognize the Least common Multiple

List the multiples the the numbers till we gain our an initial match.

### Example: discover the least usual 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 enhance at 20. That looks like this: So the least common multiple of 4 and also 10 is 20

### Example: find the least typical multiple that 6 and 15:

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

There is a enhance at 30

So the least usual multiple the 6 and 15 is 30

### Example: find the least common multiple that 4, 6, and 8

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

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

Hint: We have the right to have smaller lists because that the larger numbers.

## Least usual Multiple Tool

There is an additional method: the Least common Multiple tool does that automatically. (Yes, we waited till the end to tell you!)

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