Question

The traffic light at three different road crossing change after every 48second 72second and 108 second respectively.if they change simultaneously at 7:am,at what time will they change simultaneously again​

Answer 1

Step-by-step explanation:

Given that traffic light at three different road crossing change after every 48 seconds,72 seconds and 108 seconds respectively. Hence,after 7 min and 12 seconds they will blink simultaneously. ... If at some point they were changing simultaneously, they will continue to do so every 432 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