Discussion
3 bells beep at an interval of 30, 45 and 54 minutes. If they beep together at 11 a.m., then they will beep again together at :
Answer: B
They beep together again at 3.30 pm.
They next beep together after the least common multiple of 30, 45 and 54 minutes. With \(30 = 2 \times 3 \times 5\), \(45 = 3^{2} \times 5\) and \(54 = 2 \times 3^{3}\):
\[ \text{LCM} = 2 \times 3^{3} \times 5 = 270\ \text{minutes} \]
270 minutes is 4 hours 30 minutes, so after 11 a.m. they beep together at 3.30 p.m. 4 pm and 3 pm are half an hour out, and 4.30 pm adds 5 hours 30 minutes.
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