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

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!