At what time will traffic lights at three different crossings, changing every 48 seconds, 72 seconds, and 108 seconds respectively, change simultaneously again?

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To find out when the traffic lights will change simultaneously again, we need to calculate the least common multiple (LCM) of the three time intervals: 48 seconds, 72 seconds, and 108 seconds.

The first step is to determine the prime factorization of each time interval:

  • 48 = 24 × 31
  • 72 = 23 × 32
  • 108 = 22 × 33

Next, we take the highest power for each prime factor from the factorizations:

  • For the prime number 2: The highest power is 24 (from 48).
  • For the prime number 3: The highest power is 33 (from 108).

Now, we can calculate the LCM:

  • LCM = 24 × 33
  • = 16 × 27
  • = 432 seconds

To find out when they will change again, we convert the seconds into a more understandable format:

  • 432 seconds = 7 minutes and 12 seconds.

Thus, the traffic lights at the three different crossings will change simultaneously again after 7 minutes and 12 seconds.

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