Question

Threetraffic lights at three different road crossings change after every 48 seconds 72 second and 108 seconds if they started change is symmetry sleep at 8 a.m. after how much time will they change against simultaneously

Answer 1

Answer:

LCM of 48, 72, 108 = 432

It means traffic light again change simultaneously after 432 seconds.

432 seconds= 432/60= 7.2 minutes or 7 min 12 sec

traffic light again change simultaneously at = 8:7:12 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