There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the same point and at the same time and go in the same direction. After how many minutes will they meet again at the starting point?
Question
There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the same point and at the same time and go in the same direction. After how many minutes will they meet again at the starting point?
Solution
To solve this problem, we need to find the least common multiple (LCM) of the two given times (18 minutes and 12 minutes). The LCM of two numbers is the smallest number that is a multiple of both numbers.
Here are the steps to find the LCM:
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First, list the prime factors of each number:
- Prime factors of 18: 2, 3, 3
- Prime factors of 12: 2, 2, 3
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Then, multiply each factor the greatest number of times it occurs in either number. If the same factor occurs more than once in both numbers, you multiply the factor the greatest number of times it occurs.
- 2 occurs twice in 12 and once in 18, so you multiply by 2 twice.
- 3 occurs twice in 18 and once in 12, so you multiply by 3 twice.
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Multiply these all together: 223*3 = 36
So, Sonia and Ravi will meet again at the starting point after 36 minutes.
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