Question

The traffic light at different road crossing change after every 48 seconds , 72 seconds , 108 seconds . If they start changing simultaneously at 8 am, after how much time will they change again simultaneously

Answer 1

Answer:

08: 07 min: 12 sec AM

Step-by-step explanation:

Take LCM of 48, 72 and 108. It is equal to 432 second

432 second = 7 minute 12 second

Now 7 min 12 sec after 8 am = 8: 07 min: 12 sec 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