Question

The traffic lights at three different road crossings change after every 48 seconds, 72 seconds and 108 seconds respectively. If they change simultaneously at 7 a.m., at what time will they change simultaneously again?

Explain with working please....

Answer 1

Here's your answer

We should first take the LCM (48,72,108)
LCM(48,72,108)=2*2*2*2*3*3*3=432sec
432/60=7min12sec
The traffic light will change its colour after 7min12sec

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