Question

The traffic lights at three different road crossings change after every 48 seconds, 72 seconds and 108 seconds. If they start changing simultaneously at 8a.m., after how much time will they change again simultaneously?

Answer 1

48=2×2×2×2×3
72=2×2×2×3×3
108=2×2×3×3×3
L.C.M=2×2×2×2×3×3×3=432Second=7min12 sec.
8:00+7:12=8:07:32am

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