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
7a.m., at what time will they change simultaneously again?​

Answer 1

Step-by-step explanation:

seconds after they will change simultaneously=lcm of 48,72 and 108

=432

so time=432 seconds=7min 12 seconds

so they will change at 7:07:12 hour

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