The traffic lights at three different road crossings respectively change after every 45 seconds, 75 seconds and 100 seconds. First the traffic lights change simultaneously at 9 : 25 : 00 hours, then the time at which the lights again change simultaneously?Options10 : 05 : 009 : 40 : 009 : 45 : 459 : 50 : 00
Question
The traffic lights at three different road crossings respectively change after every 45 seconds, 75 seconds and 100 seconds. First the traffic lights change simultaneously at 9 : 25 : 00 hours, then the time at which the lights again change simultaneously?Options10 : 05 : 009 : 40 : 009 : 45 : 459 : 50 : 00
Solution
To solve this problem, we need to find the least common multiple (LCM) of the three time intervals (45 seconds, 75 seconds, and 100 seconds). The LCM of these numbers is the smallest number that is a multiple of each of them.
Step 1: Prime factorize the numbers 45 = 3^2 * 5 75 = 3 * 5^2 100 = 2^2 * 5^2
Step 2: Find the LCM The LCM is found by multiplying the highest power of all prime factors. So, LCM = 2^2 * 3^2 * 5^2 = 900 seconds
900 seconds is 15 minutes.
So, if the lights first change simultaneously at 9:25:00, they will again change simultaneously 15 minutes later, at 9:40:00.
So, the correct answer is 9:40:00.
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