Question

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

Answer 1

Answer:

LCM of 42, 72 and 108

=2\times2\times3\times3\times2\times2\times3=2×2×3×3×2×2×3

432\div60\min\ =\ 7\min\ 12\ \sec432÷60min = 7min 12 sec

hence, the lights will again change simultaneously at 7mins 12sec past 7 am.

Step-by-step explanation:

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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