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 at 7 hours 7 minutes 12 seconds in the morning, i.e., at 07:07:12 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.

We first factorize each of the numbers by prime factorization method.

From these prime factorizations, we have:

• 48 = 2 × 2 × 2 × 3
• 72 = 2 × 2 × 2 × 3 × 3
• 108 = 2 × 2 × 3 × 3 × 3

Then the LCM of 48, 72, and 108 is 2 × 2 × 3 × 3 × 3 × 2 × 2 × 1 = 432

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

432 seconds = 7 minutes and 12 seconds (This is because 432 ÷ 60 gives 7 as the quotient and 12 as the remainder).

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 at 7 a.m. + 7 minutes and 12 seconds in the morning, i.e., at 07:07:12 a.m.