What are the best ways to find the LCM in math?

Hello, I am learning how to find the LCM in math. I see two examples of how to do it. One is using multiplication and the other using prime factorization.The multiplication way takes way too long and when you have more then two numbers it takes longer. The prime factorization way looks more solid. Can someone give examples of both or suggest a better way? Also do you ever need to find the HCM in math? I have never seen an example, but does it ever happen?