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


Find the an initial Common (same) value:

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The Least common Multipleof 3 and also 5 is 15

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


So ... What is a "Multiple" ?

We gain a multiple of a number when we multiply that by an additional number. Such together multiplying through 1, 2, 3, 4, 5, etc, however not zero. As with the multiplication table. Here space some examples:


The multiples the 4 are: 4,8,12,16,20,24,28,32,36,40,44,...

You are watching: Common multiples of 5 and 10

The multiples the 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 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, and so on ..., too)

What is the "Least common Multiple" ?

It is merely the smallest that the common multiples.

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

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

recognize the Least typical Multiple

List the multiples the the numbers until we acquire our first match.


Example: find the least usual multiple that 4 and also 10:

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

Aha! over there is a enhance at 20. It looks favor this:

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So the least typical multiple that 4 and also 10 is 20


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

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

There is a enhance at 30

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


Example: discover 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 the 8 are: 8, 16, 24, 32, 40, ....

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


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

Least typical Multiple Tool

There is an additional method: the Least usual Multiple device does that automatically. (Yes, us waited till the finish to call you!)


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