The traffic lights at three different road crossings change after every 36 sec, 60 sec and 108 sec respectively. If they all change simultaneously at 7 : 20 : 00 hours, then find the time at which they will change simultaneously.Options :7:27:00 hrs7:29:00 hrs7:38:00 hrs7:42:00 hrs

To solve this problem, we need to find the least common multiple (LCM) of the three given times (36 sec, 60 sec, and 108 sec). The LCM of these numbers is the smallest time interval after which all three lights will change simultaneously.

Step 1: Prime factorization of the given numbers 36 = 2^2 * 3^2 60 = 2^2 * 3 * 5 108 = 2^2 * 3^3

Step 2: Find the LCM The LCM is found by multiplying the highest power of all prime numbers obtained from the numbers. So, LCM = 2^2 * 3^3 * 5 = 4 * 27 * 5 = 540 seconds

Step 3: Convert the LCM from seconds to minutes 540 seconds = 9 minutes

Step 4: Add the LCM to the initial time 7:20:00 + 00:09:00 = 7:29:00

So, the traffic lights will all change simultaneously at 7:29:00 hours. The correct option is 7:29:00 hrs.

To solve this problem, we need to find the least common multiple (LCM) of the three given times (36 sec, 60 sec, and 108 sec). The LCM of these numbers is the smallest number that is a multiple of each of them.

Step 1: Prime factorize the numbers 36 = 2^2 * 3^2 60 = 2^2 * 3 * 5 108 = 2^2 * 3^3

Step 2: Find the LCM The LCM is found by multiplying the highest power of all prime numbers obtained from the three numbers. So, LCM = 2^2 * 3^3 * 5 = 540 seconds

This means that the lights will all change simultaneously every 540 seconds, or 9 minutes.

Step 3: Find the next time they will change simultaneously They all changed simultaneously at 7:20:00 hours. So, the next time they will change simultaneously will be 9 minutes after that, which is 7:29:00 hours.

So, the correct answer is 7:29:00 hrs.