Aside from prime factorization, here is a method to find LCM:

list the multiples of both numbers until you reach a common one

example for 100 and 150:

The LCM  of 100 and 150 is 300.

here is an alternate method to find GCF:

List ALL factors of both numbers and highlight he greatest one

example for 138 and 102:

The GCF of 138 and 102 is 6

I prefer the prime factorization method offer these two new ones because it’s the one I had most practice with and also because in these ones there’s a lot of listing that would be exhausting to do wi really big numbers.