Question

Ben visits the park every 2 days and goes to the library every 5 days. if ben gets to do both of these today, how many days will pass before ben gets to do them both on the same day again?

Answer 1

You could label "today" as "0."

Park every 2 days:  2, 4, 6, 8, 10, 12, 14, (etc.) days
Library every 5 days:  5, 10, 15, 20 (etc.)

You can see that the smallest number of days that must go by before Ben can do both things on one day is 10.