The multiples of 3 are 3, 6, 9, 12, 15, 18, ... etcThe multiples of 5 are 5, 10, 15, 20, 25, ... etc


Find the first Common (same) value:

*


The Least Typical Multipleof 3 and also 5 is 15

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


So ... what is a "Multiple" ?

We acquire a multiple of a number when we multiply it by one more number. Such as multiplying by 1, 2, 3, 4, 5, and so on, yet not zero. As with the multiplication table. Here are some examples:


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

You are watching: What is the least common multiple of 4 and 5

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

What is a "Common Multiple" ?

Say we have detailed the initially few multiples of 4 and also 5: the widespread multiples are those that are found 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 that 20 and also 40 appear in both lists? So, the prevalent multiples of 4 and 5 are: 20, 40, (and 60, 80, etc ..., too)

What is the "Leastern Common Multiple" ?

It is simply the smallest of the common multiples.

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

... so the Least Common Multiple of 4 and also 5 is 20.

Finding the Least Typical Multiple

List the multiples of the numbers until we get our first match.


Example: Find the leastern common multiple of 4 and 10:

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

Aha! there is a complement at 20. It looks prefer this:

*

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


Example: Find the leastern prevalent multiple of 6 and also 15:

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

Tbelow is a enhance at 30

So the least prevalent multiple of 6 and also 15 is 30


Example: Find the leastern common multiple of 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 of 8 are: 8, 16, 24, 32, 40, ....

See more: Isaiah 11:6 Meaning Of And A Child Shall Lead Them Kjv, Isaiah 11:6 Kjv

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


Hint: We have the right to have actually smaller sized lists for the bigger numbers.

Leastern Typical Multiple Tool

There is one more method: the Leastern Usual Multiple Device does it immediately. (Yes, we waited until the end to tell you!)


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