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

##### 3 Answers

Least Common Multiple is

#### Explanation:

Multiples of

Multiples of

Multiples of

Hence common multiples are

and Least Common Multiple is

#### Explanation:

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

Notice that you do not even need to consider

Notice that in factor form:

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

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

#### Explanation:

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.

4, 9, and 12 all go into 36 evenly

............................

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

10 -- *thinking* -- "Won't divide by 4 or 6"

20 -- *thinking* -- "Not divisible by 6"

30 -- *thinking* -- "Won't take 4"

40 -- *thinking* -- "Not divisible by 6"

50 ---*thinking* -- "Not divisible by 4 or 6"

60 --

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.