Hello, in Math Essentials on Page 38 (LCM Drill):

I am having a hard time understanding, even from the example how you find the least common multiple through the prime factors to the highest power. I guess I don't really understand what is meant by "highest power." Can you please help explain this a bit further?

For example on #3:
What is the least common multiple of 5, 8, 12, and 15?

These put into their prime factors:
5=5
8=2*2*2
12=2*2*3
15=3*5

Now how do I get to the least common multiple or figure out what is meant by "highest power" like in the explanation on page 37 before these practice questions?

Thanks for your help!

5=5
8=2*2*2
12=2*2*3
15=3*5

Here are the numbers we're working with --
Now, the other way to think of this, other than "highest power," is the "biggest clump" of like numbers.

We know we need to have 2's, 3's, and 5's in our final answer.
Looking at the beginning numbers, the biggest clump of 2's is three 2's in the 8, so we need three 2's in our final number.
We only have a single 3 or 5 at a time, though, so our LCM is:
2^3 * 3 * 5, which is 8 * 3 * 5 which is 120.

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