X, Y, Z start at the same time in the same direction to run around a circular stadium. X completes a round in 63 seconds, Y in 105 seconds and Z in 210 seconds. If they start at the same time, then at what time will they meet again at the starting point?
Question
X, Y, Z start at the same time in the same direction to run around a circular stadium. X completes a round in 63 seconds, Y in 105 seconds and Z in 210 seconds. If they start at the same time, then at what time will they meet again at the starting point?
Solution
To solve this problem, we need to find the least common multiple (LCM) of the times it takes for each of them to complete a round. The LCM of 63, 105, and 210 seconds will give us the time it takes for all of them to meet again at the starting point.
Step 1: Prime factorize the numbers 63 = 3^2 * 7 105 = 3 * 5 * 7 210 = 2 * 3 * 5 * 7
Step 2: Find the LCM The LCM is found by multiplying the highest power of all prime numbers obtained from the numbers. So, LCM = 2^1 * 3^2 * 5^1 * 7^1 = 2 * 9 * 5 * 7 = 630 seconds
Therefore, X, Y, and Z will meet again at the starting point after 630 seconds.
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