Question

The traffic lights at three road crossings change after every 30 seconds, 45 seconds and 60 seconds. If they change together at 8:00 am, at what time will they change again simultaneously?

pls fast

Answer 1

Step-by-step explanation:

The traffic light at three different road crossing change after every 48 seconds,72 seconds and 108 seconds, respectively.

So let us take the LCM of the given time that is 48 seconds, 72 seconds, 108 seconds

⇒ 48 = 2 × 2 × 2 × 2 × 3

⇒ 72 = 2 × 2 × 2 × 3 × 3

⇒ 108 = 2 × 2 × 3 × 3 × 3

Hence, LCM of 48, 72 and 108 = (2 × 2 × 2 × 2 × 3 × 3 × 3)

LCM of 48, 72 and 108 = 432

So  after 432 seconds, they will change simultaneously

We know that

60 seconds = 1 minute

so on dividing 432 / 60, we get 7 as quotient and 12 as a reminder

Hence, 432 seconds = 7 min 12 seconds

∴ The time  = 7 a.m. + 7 minutes 12 seconds

Hence, the lights change simultaneously at  7:07:12 a.m

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