Question

the traffic lights at three different road crossing change after every 48 seconds, 72 seconds , and 180 seconds respectively. if they change simultaneously at 7 am,at what time will they change simultaneously again? ​

Answer 1

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

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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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