Question

the traffic lights at three different crossings change after every 48 72 108 seconds respectively if the change simultaneously at 8:00 a.m. at what time will they change together again

Answer 1

The traffic lights will change together again at 8:07 a.m. and 12 seconds.

Step-by-step explanation:

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

The prime factors of the numbers are:

• 48: 2, 2, 2, 2, 3
• 72: 2, 2, 2, 3, 3
• 108: 2, 2, 3, 3, 3

To find the LCM, we take the highest power of each prime factor that appears in the factorization of any of the numbers:

LCM = 2^4 x 3^3 = 16 x 27 = 432 seconds.

Since there are 60 seconds in a minute, we can divide 432 by 60 to find the number of minutes: 432 ÷ 60 = 7 remainder 12.

Adding this remainder to the start time of 8:00 a.m., we get that the traffic lights will change together again at 8:07 a.m. and 12 seconds.