Question

Explain when you would use each method (finding multiples or prime factorization) for finding the LCM and shy

Answer 1

For example, the LCM of 10, 30, 45 is 5.
List out the prime factorization of all 3 numbers. 
10=2*5
30=2*3*5
45=3*3*5
As you can see, in all 3 prime factorizations, 5 is the biggest, and the only prime number present in all of the listed prime factorizations. Hope this answers your question!