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?

Time-period after which these lights will change = LCM of 48, 72 and 108

LCM is the lowest common multiple. LCM of two numbers It is the smallest number that is divisible by both of them.

LCM = 2 × 2 × 2 × 2 × 3 × 3 × 3 = 432

The lights will change together after every 432 seconds.

60 seconds = 1 minute

432 seconds = 432/60 = 7 minutes and 12 seconds

Hence these lights will change simultaneously again at 7:07:12 am.