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


Find the very first Common (same) value:

*


The Least common Multipleof 3 and also 5 is 15

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


So ... What is a "Multiple" ?

We obtain a multiple of a number as soon as 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 are some examples:


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

You are watching: Multiples of 5 up to 100

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

What is a "Common Multiple" ?

Say we have provided the first couple of multiples that 4 and also 5: the common multiples space those that are discovered 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 40 appear in both lists? So, the usual multiples of 4 and 5 are: 20, 40, (and 60, 80, and so on ..., too)

What is the "Least usual Multiple" ?

It is simply the smallest of the typical multiples.

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

... Therefore the Least typical Multiple that 4 and also 5 is 20.

finding the Least usual Multiple

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


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

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

Aha! over there is a match at 20. The looks like this:

*

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


Example: uncover the least common multiple that 6 and also 15:

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

There is a complement at 30

So the least typical multiple that 6 and 15 is 30


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

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

See more: How Long Can You Freeze Cooked Turkey Breast ? Freezing Leftover Turkey

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


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

Least common Multiple Tool

There is another method: the Least common Multiple device does that automatically. (Yes, us waited till the end to phone call you!)


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