Question

The traffic lights at three different road crossings change after every 48 seconds, 72 seconds and 108 seconds respectively. If they cahnbge simultaneously at 7.Am at what time will they change simultaneously again?

Answer 1

Answer:

Step-by-step explanation:

lcm of 72,48 and 108

lcm= product of greatest power of each prime factor

72= 2³×3²; 48=2³×2×3; 108=2²×3³

hence lcm=2³×2×3³=16×27=432 sec=432÷60 min

=7.2 min i.e 7 minutes and 12 seconds.

so the traffic lights will change simultaneously at 7:7:12 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