Question

The traffic lights at three different road
crossings change after every 48 seconds,
72 seconds and 108 seconds respectively. If they
change simultaneously at 8 a.m., at what time
will they change together again?
​

Answer 1

Step-by-step explanation:

To calculate the timing at which all of these three light, We need to calculate the LCM

LCM (72,48,108)

= 432 seconds

So lights will change together in 432 seconds (7minutes and 12 seconds)

So they will change together again on 8:07:12

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