Question

An electric sign contains three flashing lights,red, yellow and green, the red light flashes on every 10 seconds, the yellow light flashes on every 15 seconds and the green light flashes on every 18 seconds. If they are switched on together, after how many seconds will they be on together again

Answer 1

We know that the red light flashes every 10 seconds, the yellow light flashes on every 15 seconds and the green light flashes on every 18 seconds. So we should find the least common multiple (M) of numbers 10, 15 and 18, because it is the smallest number that divides on all of these numbers.

$10=2\cdot5, \; 15 = 3\cdot 5, \; 18 = 2\cdot3^2 \; \Rightarrow \; M = 2\cdot3^2\cdot5 = 90.$ Therefore, after 90 seconds these lights will be together again.