Reinventing a very small wheel

So I just came up with a brilliant way to find the least common multiple of a set of numbers. Say you have:

1,2,3,4,5

And you want to find the least common multiple of them all. First convert each to a prime factorization.

1 = 1
2 = 1*2
3 = 1*3
4 = 2*2
5 = 1*5

Now, just take each prime factor the most times it appears in any entry, and use it that many times, and multiply them all together.

LCM = 1*2*2*3*5 = 60

Anyhow, I googled it, and found that this is the standard way it's supposed to be taught. I'm positive that I dodged this bit of information in my fairly extensive math background, and I'm not sure how.

At least now I'm sure that I agree with it.