Question

The traffic lights at three different roads change after every 12,24 and 72 seconds respectively. If they change simultaneously at 7:15 a.m.,at what time they will change again?
Please answer asap

Answer 1

Answer: The lights change simultaneously at  7:07:12 a.m

Step-by-step explanation:

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