A, B and C start at the same time in the same direction to run around a circular stadium. A completes a round in 252 seconds, B in 308 seconds and c in 198 seconds, all starting at the same point. After what time will they again at the starting point ?*4 points42 minutes and 36 seconds26 minutes and 18 seconds46 minutes and 12 seconds45 minutes
Question
A, B and C start at the same time in the same direction to run around a circular stadium. A completes a round in 252 seconds, B in 308 seconds and c in 198 seconds, all starting at the same point. After what time will they again at the starting point ?*4 points42 minutes and 36 seconds26 minutes and 18 seconds46 minutes and 12 seconds45 minutes
Solution
To solve this problem, we need to find the least common multiple (LCM) of the times taken by A, B, and C to complete a round. The LCM will give us the time after which all three will again be at the starting point.
The times taken by A, B, and C are 252 seconds, 308 seconds, and 198 seconds respectively.
First, let's find the LCM of these three numbers.
The prime factorization of 252 is 2^2 * 3^2 * 7. The prime factorization of 308 is 2^2 * 7 * 11. The prime factorization of 198 is 2 * 3^2 * 11.
To find the LCM, we take the highest power of each prime from the factorizations:
LCM = 2^2 * 3^2 * 7 * 11 = 924 seconds.
So, they will all be at the starting point again after 924 seconds.
To convert this into minutes and seconds, we divide by 60 (since there are 60 seconds in a minute):
924 seconds = 15 minutes and 24 seconds.
So, the correct answer is not listed among the options provided.
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