Question

The traffic. Lights at three road crossings change after after every 48 seconds 72 seconds and 108 seconfs if they start changing simutaneously at 8 am after how much time they will change again simutaneously
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Answer 1

Answer:

7:7:12am

Step-by-step explanation:

Given that traffic light at three different road crossing change after every 48 seconds,72 seconds and 108 seconds respectively.

48 = 2 × 2 × 2 × 2 × 3

72 = 2 × 2 × 2 × 3 × 3

108 = 2 × 2 × 3 × 3 × 3

Hence LCM of 48, 72 and 108 is (2 × 2 × 2 × 2 × 3 × 3 × 3)

= 432

That is after 432 seconds they will change simultaneously

432 seconds = 7 min 12 seconds

Thus the traffic lights change simultaneously at 7:7:12 am

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