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 also 5, and is the smallest number like that.)

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

We obtain a multiple that a number once we multiply that by an additional number. Such as multiplying by 1, 2, 3, 4, 5, etc, yet not zero. As with the multiplication table. Here room some examples:

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

## What is a "Common Multiple" ?

Say us have listed the first few multiples of 4 and also 5: the common multiples room those that are uncovered in both lists:

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

## What is the "Least usual Multiple" ?

It is merely the smallest that the common multiples.

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

... For this reason the Least usual Multiple that 4 and also 5 is 20.

## finding the Least usual Multiple

List the multiples that the numbers until we gain our first match.

### Example: find the least typical 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 complement at 20. That looks choose this: So the least typical multiple of 4 and also 10 is 20

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

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

There is a complement at 30

So the least typical multiple of 6 and also 15 is 30

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

Multiples that 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: How Far Is Birmingham Alabama To Atlanta Georgia, Atlanta To Birmingham Distance (Atl To Bhm)

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

Hint: We can have smaller sized lists for the enlarge numbers.

## Least common Multiple Tool

There is another method: the Least usual Multiple tool does the automatically. (Yes, us waited until the finish to phone call you!)

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