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Mathematics

Traffic lights at three different road crossing change after 48 seconds, 72 seconds and 108 seconds respectively. At what time will they change together again if they change simultaneously at 7 A.M.?

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Answer

The required time interval after which the traffic lights will change together again is the LCM of 48, 72 and 108.

248, 72, 108
224, 36, 54
212, 18, 27
26, 9, 27
33, 9, 27
31, 3, 9
31, 1, 3
1, 1, 1

LCM of 48, 72 and 108 = 2 × 2 × 2 × 2 × 3 × 3 × 3 = 432 seconds.

Converting to minutes: 432 seconds = 7 minutes 12 seconds.

The traffic lights change simultaneously at 7 A.M. So they will change together again at:

7 A.M. + 7 min 12 sec = 7:07:12 A.M.

Hence, they will change together again at 7 minutes 12 seconds past 7 A.M.

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