Question

The traffic lights at the different road crossing change after every 48 seconds 72
seconds and 108 seconds respectively. If they change simultaneously at
7am what time will they change simultaneously again?
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Answer 1

Answer:

The traffic lights at three different roads crossing change after every 48 seconds, 72 seconds, and 108 seconds. How often will they change simultaneously? It depends. If at some point they were changing simultaneously, they will continue to do so every 432 seconds.

Step-by-step explanation:

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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