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Real Numbers

Question

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There is a circular path around a sports Held. Priya takes 18 minutes to drive one round of the Held, 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

Required number of minutes is the LCM of 18 and 12. Thus,

Since, 18 = 2 × 3 × 3 = 2 × 3²

and 12 = 2 × 2 × 3 = 2² × 3

∴ LCM = Product of each prime factor with highest power

= 2² × 3² = 36

Hence, Ravi and Priya will meet again at the starting point after 36 minutes.

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