The number system

Question

The light on a cell phone tower blinks every five seconds The light on the water tower blinks every eight seconds. The lights blink at the same time. How many seconds will pass before the two lights blink together again?

Answer 1

Let time 0 be the moment the two lights blink together.

The next occurrence will be at a time where 5 and 8 are common factors. The first time that will happen is at 40 seconds, because 8*5 = 40. The two lights will blink simultaneously every 40 seconds.

Cell tower blinks at 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, ...

Water tower blinks at 0, 8, 16, 24, 32, 40, 48, ...