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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?**

Answer:

**Solutions: Given, Sonia takes to complete a round = 18 minutes
Ravi takes to complete a round = 12 minutes. **

**Since, LCM of two or more numbers = product of the greatest power of each prime factor involved in the numbers, with the highest power.**

**Let us find the LCM of 18 and 12**

**We have**

**18 = 2 × 3 × 3 = 2 × 3²**

**12.= 2 × 2 × 3 = 2² × 3**

**LCM (18,12) = 2² × 3² = 36**

**After 36 minutes Sonia will be at the starting point after completing 2 rounds of the field and Ravi also be at some point after 3 rounds. **

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