There is a circular path around a sports field. Semistakes 18 minutes to drive one and of the Red
takes 12 minutes for the same. Suppose they both start at the same point and at the same time, and get the
same direction. After how many minutes will they meet again at the starting points ?
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Time taken by semistakes to drive one round= 18 minutes
Time taken by red to drive one round= 12 minutes
Time taken by both to meet again = LCM of 18 & 12
we find LCM of 18 & 12 by prime factorization
LCM:
18 = 2 × 3 × 3
= 2^1 × 3^2
12 = 2 × 2 × 3
= 2^2 × 3^1
LCM = Product of greatest power of each prime factor
2^2 × 3^2
= 4 × 9 = 26
Hence, time taken by both to meet again
= LCM of 18 & 12 = 36 minutes.
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