Question

The traffic lights at three different road crossings change after every 48 72 and 108 seconds respectively if they change simultaneously at 8am, at what time will they change together again

Answer 1

here is the solution

Explanation:

First find the LCM of 48,72 and 108.

The LCM is 432.

Now convert 432 to minutes.

432 seconds is 12.5 minutes.

Now add 12.5minutes to 8am.

The three traffic will change simultaneously at half a minute after 8:12 .

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