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


Find the very first Common (same) value:

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The Least common Multipleof 3 and 5 is 15

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


So ... What is a "Multiple" ?

We get a multiple the a number once we multiply that by another number. Such together multiplying through 1, 2, 3, 4, 5, etc, yet not zero. Similar to 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: Lowest common multiple of 4 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 noted the first few multiples that 4 and 5: the common multiples room those that are discovered in both lists:


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

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

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

recognize the Least typical Multiple

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


Example: discover the least common multiple of 4 and also 10:

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

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

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


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

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

There is a complement at 30

So the least common multiple of 6 and 15 is 30


Example: find the least typical multiple of 4, 6, and 8

Multiples the 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 Many Legs Does Cockroaches Have ? How Many Legs Do Cockroaches Have

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


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

Least common Multiple Tool

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


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