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

Answer 1

7:02 am

Step-by-step explanation:

48+72=120

sooooo………

120seconds=2 minutes

and 7:00+0:02minutes=7:02 am…

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Answer 2

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If the traffic lights change simultaneously at 7 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:

7 am + 7 minutes 12 seconds

07 : 07 : 12 am