The traffic lights at three different road crossing 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?

The traffic lights will change at the LCM of intervals of all the three lights.

So LCM of 48, 72 and 108 -


Prime factors of the numbers are -


48 = 2 × 2 × 2 × 2 × 3


72 = 2 × 2 × 2 × 3 × 3


108 = 2 × 2 × 3 × 3 × 3


So LCM = product of prime factors with highest powers = 24 × 33 = 432


traffic light will change after 432 seconds.


We know 1 min = 60 seconds,


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


the next time lights will simultaneously change at 8:7:12 hrs.


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