Question

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

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Answer 1

Answer:

We know that in order to find the time when the three lights will change simultaneously again after 7 a.m., we need to find the LCM of 48, 72, and 108. Hence, converting 432 seconds into minutes and seconds, we get: 432 seconds = 7 minutes and 12 seconds.

Answer 2

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If the traffic lights change simultaneously at 7 a.m, then they will change simultaneously again after the LCM of the duration i.e. 48 s, 72 s and 108 s.

LCM of these durations by prime factorisation

48 = 2 × 2 × 2 × 2 × 3 = 2⁴ × 3

72 = 2 × 2 × 2 × 3 × 3 = 2³ × 3²

108 = 2 × 2 × 3 × 3 × 3 = 2² × 3³

LCM of 48, 72 and 108 is 2⁴ × 3³ = 432 seconds.

Hence, They will change after 432 seconds i.e. 7 minutes 12 seconds.

The traffic lights will change after:

7 am + 7 minutes 12 seconds

07 : 07 : 12 am