Question

the traffic lights at three different road crossing change after every 48 sec , 72 sec , and 108 sec respectively . if they all change simultaneously at 8 hours , at what time will they again change simultaneously ?

Answer 1

they again change simultaneously in 228 sec

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