A red light flashes every 3 seconds. A yellow light flashes every 8 seconds. A green light flashes evey 11 seconds. They all flash at the same time.

Question

A red light flashes every 3 seconds. A yellow light flashes every 8 seconds. A green light flashes evey 11 seconds. They all flash at the same time. After how many seconds will they next all flash at the same time.

Answer 1

"After how many seconds" means that we start timing (t=0 seconds) when the three lights flash at the same time.

 

At the "next" time that they all flash together, t=x seconds:

       x is a multiple of 3

and  x is a multiple of 8

and  x is a multiple of 11

and to be "next" it must be the least common multiple (LCM).

 

3 is prime

8 = 2*2*2

11 is prime

 

The fewest factors for a number that 3 and 8 and 11 divide into evenly are 3*2*2*2*11.  That is, the next time that the three lights will flash together is at t = 264 seconds.