Question

The traffic lights at four different road Crossings change after every 24 second 48 second 72 second and 108 seconds effectively if they change simultaneously at 8:00 a.m. at what time will they changes simultaneously again

Answer 1

At 8:00 AM + the LCM of the time-in-between-change for each of the crossings.

LCM = 432 seconds = 7 minutes and 12 seconds.

So, they will change simultaneously again at 8:07:12 AM.

Answer 2

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If the traffic lights change simultaneously at 8 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:

8 am + 7 minutes 12 seconds

08 : 07 : 12 am