The least common multiple, or LCM, of a group of numbers, is the smallest (least) number that is a multiple of each of the numbers of that given set.

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Finding the LCM goes as follows:

First, list all multiples of each number in the set of numbers that are given.

Then, list all multiples that they have in common.

Then, pick the least of all multiples that are they have in common.

For example, find the LCM (least common multiple) of 12 & 16.

Here’s the solution:

First, list all multiples of 12 & 16:

The multiples of 12 are: 12, 24, 36, 48, 60, 72, 84, 96, . . .

The multiples of 16 are: 16, 32, 48, 64, 80, 96, 112, . . .

Now, pick all common multiples.

The common multiples are: 48, 96, . . .

So the LCM of 12 and 16 is the least of these common multiples.

The LCM of 12 and 16, or LCM (12,16), is 48.

One more example: Find the LCM (least common multiple) of 6 & 9:

The multiples of 6 are: 6, 12, 18, 24, 30, 36, 42, 48, 54,

The multiples of 9 are: 9, 18, 27, 36, 45, 54, 63, 72,…

The common multiples are: 18, 54, …

As before, the LCM is the least (or smallest) of these common multiples.

So we write: LCM(6,9) = 18

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