Question: Two friends, Alice and Bob, go for a run around a circular track. Alice completes one lap every 8 minutes, and Bob completes one lap every 12 minutes. If they both start at the same time, after how many minutes will they meet at the starting point again?
(A) 12 minutes
(B) 16 minutes
(C) 24 minutes
(D) 48 minutes
Solution:
We need to find the LCM of 8 and 12.
Prime factorization of 8:
8=2³
Prime factorization of 12:
12=2²×3
LCM is the product of the highest powers of all prime factors:
LCM(8,12) = 2³ ×3 = 8 × 3 = 24
So, Alice and Bob will meet at the starting point again after 24 minutes.
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