the traffic lights at three different road Crossings change after every 48 seconds 72 seconds and 18 seconds respectively if they all change at a 2000 hours then when will they again change at
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LCM of 48 72 18
144 sec
144 / 60
2hrs: 40 minutes
They again change
20 hrs + 2 hrs : 40 minutes
22hrs : 40 minutes
144 sec
144 / 60
2hrs: 40 minutes
They again change
20 hrs + 2 hrs : 40 minutes
22hrs : 40 minutes
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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
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