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


Find the first Common (same) value:

*


The Least usual Multipleof 3 and also 5 is 15

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


So ... What is a "Multiple" ?

We gain a multiple of a number as soon as we multiply the by one more number. Such together multiplying through 1, 2, 3, 4, 5, etc, however not zero. As with the multiplication table. Here room some examples:


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

You are watching: What are common multiples of 4 and 6

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

What is a "Common Multiple" ?

Say us have noted the first couple of multiples that 4 and 5: the common multiples space those the are discovered in both lists:


The multiples the 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 also 40 show up in both lists? So, the typical multiples of 4 and also 5 are: 20, 40, (and 60, 80, and so on ..., too)

What is the "Least typical Multiple" ?

It is simply the smallest that the usual multiples.

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

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

finding the Least usual Multiple

List the multiples the the numbers till we acquire our very first match.


Example: uncover the least common multiple that 4 and also 10:

The multiples the 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 favor this:

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So the least common multiple the 4 and 10 is 20


Example: uncover the least usual multiple that 6 and 15:

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

There is a match at 30

So the least typical multiple that 6 and 15 is 30


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

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

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


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

Least usual Multiple Tool

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


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