Multiple Ages

Determine my age given that it is a multiple of a particular integer one year and a multiple of a different integer the next year.


My age this year is a multiple of 7. Next year it will be a multiple of 5. When will this event occur again?

Extension
My age this year is a multiple of x. Next year it will be a multiple of x – 2. When will this event occur again? Give your answer in terms of x.

(Source: Adapted from Mathematics Teaching in the Middle School, Nov-Dec 1996)