Question

The traffic lights at three different road crossings change after every 48 seconds, 72 seconds and 108 seconds respectively. If they all change simultaneously at 8 a.m., then at what time will they again change simultaneously?

Answer 1

The traffic lights at three different road crossings change after every 48 seconds, 72 seconds and 108 seconds respectively.

Find the LCM of 48, 72 and 108:

48 = 2 × 2 × 2 × 2 × 3 = 2⁴ × 3

72 = 2 × 2 × 2 × 3 × 3 = 2³ × 3²

108 = 2 × 2 × 3 × 3 × 3= 2² × 3 ³

LCM = 432 or 432 sec

Convert into mins:

432 sec = 7 mins 12 sec

So, at 8:7:12 hrs traffic lights will again change.