Question

The traffic lights at three different road crossings change after every 48 seconds, 72 seconds, and 108 seconds respectively. If they change simultaneously at 7 a.m., at what time will they change simultaneously again?

Answer 1

The time period after which these lights will change = LCM of 48, 72, 108

2	48, 72, 108
2	24, 36, 54
2	12, 18, 27
2	6, 9, 27
3	3, 9, 27
3	1, 3, 9
3	1, 1, 3
	1, 1, 1

LCM = 2 × 2 × 2 × 2 × 3 × 3 × 3 = 432

They will change together after every 432 seconds i.e., 7 min 12 seconds.

Hence, they will change simultaneously at 7: 07: 12 am.