How would I solve this?

Question

A pet store owner changes the water in a fish tank every 45 days and changes the pump filter every 20 days. If the water and filter are changed on the same day, in how many days will they be changed again together.

Answer 1

Call the day they change both of them t = 0. Every 45 days the owner changes the fish tank. So when t = 0, 45, 90, 135... , the owner changes the fish tank. Notice, that each of these days are multiples of 45.

The pet owner changes the pump filter every 20 days. So every day that is a multiple of 20, the owner changes the pump filter.

The owner will change both, when the day is a multiple of both 20 and 45. So you're looking for a common multiple of 20 and 45. You're also looking for the first time the owner changes both, so what you'll need is the least common multiple of 20 and 45.