Question

We observed the traffic lights at three different squares on the same big road. They turn green every 60 seconds, 120 seconds and 24 seconds. When the signals were switched on at 8 o’clock in the morning, all the lights were green. How long after that will all three signals turn green simultaneously again?

Answer 1

All the three signals would turn green simultaneously again at a time which is a multiple of the three intervals of 60 seconds, 120 seconds, and 24 seconds. So, all three signals turn green simultaneously again after a time interval which is the LCM of 60 seconds, 120 seconds, and 24 seconds.
Multiples of 60: 60, 120, 180, 240,...
Multiples of 120: 120, 240,...
Multiples of 24: 24, 48, 72, 96, 120, 144, 168,...
Common multiples of 60, 120, and 24: 120, 240,...
∴ All the three signals turn green simultaneously again = LCM of the time intervals 60 seconds, 120 seconds and 240 seconds = 120 seconds

Since, 60 seconds = 1 minute

∴ 120 seconds = 2 minutes

Thus, all three signals turn green simultaneously again after 120 seconds.