Question

Traffic lights at three different road crossing change after every 48 seconds, 72 secondsand 108 seconds... If they start changing simultaneously at 8 am how much time will they change simultaneously

Answer 1

Answer:

8:07:12

Step-by-step explanation:

If we find the LCM of the timings we can find how much time they will ring together after.

LCM of 48, 72 and 108 is 432 seconds

i.e. 7 mins 12 seconds.

Therefore the bell will ring at 8:07:12

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