What is the LCM for 4, 9, 12?
Hence common multiples are
and Least Common Multiple is
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
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"
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.