The traffic lights at three different road crossings change after every 48 sec, 72 sec and 108 sec respectively. If they all change simultaneously at 8:20:00 hrs, when will they change again simultaneously
Question
The traffic lights at three different road crossings change after every 48 sec, 72 sec and 108 sec respectively. If they all change simultaneously at 8:20:00 hrs, when will they change again simultaneously
Solution
To solve this problem, we need to find the least common multiple (LCM) of the three given times (48 sec, 72 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 48 = 2^4 * 3 72 = 2^3 * 3^2 108 = 2^2 * 3^3
Step 2: Find the LCM The LCM is found by multiplying the highest power of all prime factors obtained from the numbers. So, LCM = 2^4 * 3^3 = 16 * 27 = 432 seconds
This means the lights will all change together every 432 seconds.
Step 3: Convert the LCM to minutes and seconds 432 seconds = 7 minutes and 12 seconds
Step 4: Add this time to the initial time 8:20:00 + 00:07:12 = 8:27:12
So, the traffic lights will all change again simultaneously at 8:27:12 hrs.
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