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 7a.m., at what time will they change simultaneously again? ​

Answer 1

Answer:

after 14 minutes and 24 seconds

= 7:14:24 am

Step-by-step explanation:

after 864 seconds they change simultaneously again

864 seconds = 14 minutes and 24 seconds

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