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


Find the very first Common (same) value:

*


The Least usual Multipleof 3 and also 5 is 15

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


So ... What is a "Multiple" ?

We acquire a multiple the a number when we multiply that by another number. Such together multiplying by 1, 2, 3, 4, 5, etc, however not zero. Similar to the multiplication table. Here room some examples:


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

You are watching: The least common multiple of 3 and 5

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 uncovered in both lists:


The multiples that 4 are: 4,8,12,16,20,24,28,32,36,40,44,...
The multiples the 5 are: 5,10,15,20,25,30,35,40,45,50,...

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

What is the "Least common Multiple" ?

It is simply the smallest of the typical multiples.

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

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

finding the Least common Multiple

List the multiples that the numbers until we acquire our an initial match.


Example: uncover the least usual multiple the 4 and also 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:

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So the least common multiple of 4 and also 10 is 20


Example: uncover 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 match at 30

So the least usual multiple that 6 and also 15 is 30


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

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

See more: The Difference Between Galvanic And Voltaic Cell S, Electrochemistry

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


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

Least common Multiple Tool

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


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