Question

the traffic lights at three different road crossings change after every 48 sec 72 sec and 108 sec respectively. if they all change simultaneously at 8.20.00 hours,then at what time they again change simultaneously.​

Answer 1

Answer:

the traffic lights at three different road crossings change after every 48 sec 72 sec and 108 sec respectively. if they all change simultaneously at 8.20.00 hours,then at what time they again change simultaneously.

Answer 2

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If the traffic lights change simultaneously at 8:20 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 + 27 minutes 12 seconds
• 08 : 27 : 12 am