Answer to Question #299669 in Combinatorics | Number Theory for OMAR

Question

Three neon lights colored red, blue and green flash at different time intervals. The red light flashes after every 18 seconds and the green light after every 15 seconds. If all the three lights flash together at 8:00 am, how many times will all three lights flash together by 9:30 am.

Please show your full steps answer.

Answer 1

First we determine the LCM of the times in which the three neon lights flashes. The red light flashes after every 24 seconds, the blue light flashes after every 18 seconds and the green light flashes after every 15 seconds.

The LCM of the times after which the three neon lights flashes is 360 seconds=6minutes.

The time between 8:00 and 9:30 am is 1hour 30 minutes which is equivalent to 60+30=90 minutes.

The number of times the three lights flash together between 8:00 am and 9:30am is ${90\over6}=15$ times