Numbers that are divisible So I am given the following question: For natural numbers less than or equal to 120, how many are divisible by 2, 3, or 5? I solved it by inclusion-exclusion principle and by using the least common multiple by having it as (2, 3, 5)=120 which is equal to 30. Are these the right way to solve them or is there other ways?

Inclusion-exclusion is a good choice (and I expect your teacher intended you to use this method).
However, in mathematics, there are often many methods you can use.  For instance, we could instead find the answer computationally (in GAP this can be found by Number([1..120],i->i mod 2=0 or i mod 3=0 or i mod 5=0);).
There is no "best" method.  In fact, it's usually best to use multiple methods in order to perform cross-checking.
