Question: Two machines are running at different intervals. Machine A runs every 16 minutes, and Machine B runs every 24 minutes. If both machines start running together at 8:00 AM, at what time will they both run together again?
(A) 8:16 AM
(B) 8:24 AM
(C) 8:48 AM
(D) 9:12 AM
Solution:
We need to find the LCM of 16 and 24.
Prime factorization of 16:
16 = 2⁴
Prime factorization of 24:
24 = 2³×3
LCM is the product of the highest powers of all prime factors:
LCM (16,24) = 2⁴×3 = 16×3 = 48
So, the machines will run together again after 48 minutes, which is 8:48 AM.
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