Factors and primes

Question

I wanted to know if anyone could explain how to work out this question.

$n$ is a (natural) number. 100 is the $LCM$ of 20 and $n$. Work out two different possible values for $n$.

Answer 1

$100$ is the LCM of $20$ and $n$. Hence, $100$ must be a multiple of $n$, so we only need to look at divisors of $100$ as possible values of $n$.

Furthermore, divisors of $20$ will lead to $20$ as LCM of $n$ and $20$ and not $100$, so they can be ruled out.

We are left with $n = 25$, $n = 50$ and $n = 100$.

Edit: I would like to note that in THIS case, all three possibilities are solutions, however, this is not generally true. Don't forget to check the possibilities that are left over.