Question

The traffic light at three different road crossings change after every 48 sec, 72 sec 108 respectively . If they all change simultaneously at 8.20 hrs, when will they again change simultaneously ?

Answer 1

Answer:

they will again change at 9:08 hours

Answer 2

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If the traffic lights change simultaneously at 8:20 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 + 27 minutes 12 seconds

08 : 27 : 12 am