Question : Three electronic devices make a beep every 48 seconds, 72 seconds and 108 seconds respectively. They beeped together at 10 a.m. The time when they will next make a beep together, at the earliest, is:
Option 1: 10: 07: 12 a.m
Option 2: 10: 07: 24 a.m
Option 3: 10: 07: 36 a.m
Option 4: 10: 07: 48 a.m
Correct Answer: 10: 07: 12 a.m
Solution :
48 = 2 × 2 × 2 × 2 × 3
72 = 2 × 2 × 2 × 3 × 3
108 = 2 × 2 × 3 × 3 × 3
So, LCM = 2 × 2 × 2 × 2 × 3 × 3 × 3 = 432
432 seconds = 7 minutes and 12 seconds
They beeped together at 10 a.m.
They beep together again after 7 minutes 12 seconds, i.e., at 10:07:12 a.m.
Hence, the correct answer is 10: 07: 12 a.m.
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