# What is the LCM for 4, 9, 12?

Least Common Multiple is

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Write each number as the product of its prime factors, then you know what you are working with.

Notice that in factor form:

All the numbers are in the LCM, but there are no unnecessary factors.

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Here's a fast and easy way to find LCMs and LCDs

Start with the largest figure. In this case, that is 12.

You know that the LCM has to be some multiple of 12, so start considering the multiples of 12 one at a time.

Here's another example Find the LCM of 4, 6, and 10

Don't waste your time fooling around with prime factors. Instead, just rapidly consider each multiple of 10 until you hit on the one that works

This usually takes only a few seconds, and you should always do it this way when the numbers let you.

If the numbers are too hard to work with like this, you can always just go back to finding prime factors again.

But the first choice of the way to find LCMs and LCDs should be just thinking in turn about each multiple of the largest figure.

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The least common multiple (LCM) for 4, 9, and 12 is 36.

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