# what time the traffic lights will change simultaneously again?

## 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?

## Answer: The three lights will change simultaneously again after 7 a.m. at 7:07:12 a.m.

## Explanation:

We know that in order to find the time when the three lights will change simultaneously again after 7 a.m., we need to find the LCM of 48, 72, and 108.

Finding the LCM using the prime factorization method, we get the prime factors of LCM as :

Factors = 2 × 2 × 3 × 3 × 3 × 2 × 2 × 1 × 3 = 432

Hence, converting 432 seconds into minutes and seconds, we get:

432 seconds = 7 minutes and 12 seconds.

Thus, the three lights will change simultaneously again after 7 a.m. at 7:07:12 a.m.

### Thus, The three lights will change simultaneously again after 7 a.m. at 7 a.m. + 7 minutes and 12 seconds = 7:07:12 a.m.

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