The multiples the 3 room 3, 6, 9, 12, 15, 18, ... EtcThe multiples that 5 room 5, 10, 15, 20, 25, ... Etc


Find the first Common (same) value:

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The Least usual Multipleof 3 and also 5 is 15

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


So ... What is a "Multiple" ?

We acquire a multiple the a number as soon as we multiply the by an additional number. Such together multiplying by 1, 2, 3, 4, 5, etc, but not zero. As with 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: Which number is a multiple of 8

The multiples of 5 are: 5,10,15,20,25,30,35,40,45,50,...

What is a "Common Multiple" ?

Say us have provided the first couple of multiples that 4 and also 5: the common multiples are those that are uncovered 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 that 20 and also 40 show up in both lists? So, the common multiples of 4 and also 5 are: 20, 40, (and 60, 80, and so on ..., too)

What is the "Least common Multiple" ?

It is merely the smallest of the typical multiples.

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

... Therefore the Least usual Multiple the 4 and also 5 is 20.

recognize the Least usual Multiple

List the multiples of the numbers till we get our an initial match.


Example: discover the least typical multiple that 4 and 10:

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

Aha! over there is a match at 20. That looks prefer this:

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So the least usual multiple the 4 and also 10 is 20


Example: find the least typical multiple of 6 and also 15:

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

There is a match at 30

So the least common multiple the 6 and also 15 is 30


Example: uncover the least common multiple of 4, 6, and 8

Multiples the 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 Many Inches Is 174 Cm To In, How Many Feet And Inches In 174 Cm

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


Hint: We deserve to have smaller lists for the larger numbers.

Least common Multiple Tool

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


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