The multiples that 3 are 3, 6, 9, 12, 15, 18, ... EtcThe multiples of 5 space 5, 10, 15, 20, 25, ... Etc

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

(15 is a lot of of both 3 and also 5, and is the the smallest number prefer that.)

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

We obtain a multiple that a number once we multiply that by another number. Such as multiplying by 1, 2, 3, 4, 5, etc, yet not zero. Similar to the multiplication table. Here space some examples:

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

## What is a "Common Multiple" ?

Say us have noted the first couple of multiples the 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 that 5 are: 5,10,15,20,25,30,35,40,45,50,...

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

## What is the "Least typical Multiple" ?

It is simply the smallest the the typical multiples.

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

... So the Least common Multiple the 4 and 5 is 20.

## detect the Least usual Multiple

List the multiples the the numbers till we acquire our very first match.

### Example: discover the least common multiple that 4 and also 10:

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

Aha! over there is a match at 20. It looks choose this: So the least usual multiple the 4 and 10 is 20

### Example: discover the least typical multiple of 6 and 15:

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

There is a match at 30

So the least common multiple that 6 and 15 is 30

### Example: discover the least typical multiple the 4, 6, and 8

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

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

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

## Least typical Multiple Tool

There is another method: the Least typical Multiple tool does the automatically. (Yes, we waited until the finish to tell you!)

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