Question

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

Answer:

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

Taking LCM for,

48, 72 and 108 i.e (2 × 2 × 2 × 2 × 3 × 3 × 3)= 432

We have,

432 seconds = 7 min 12 seconds

Hence,after 7 min and 12 seconds they will blink simultaneously.

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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