Discussion
Three alarm clocks ring their alarms at regular intervals of 20, 21 and T minutes respectively. If the clocks beep together at 12 noon, for which value of T would they beep together again at the earliest ?
Answer: C
The clocks beep together soonest when T is 28 minutes.
They beep together again after the least common multiple of the three intervals. For 20 and 21 alone that is 420 minutes. A value of T that already divides 420 adds nothing, so the clocks meet again at 420 minutes, 7 P.M.
\[ \begin{aligned} 28 = 4 \times 7, \ 420 &= 28 \times 15 \\ \text{LCM}(20, 21, 28) &= 420 \end{aligned} \]
The other choices push the meeting later: T = 8 gives 840 minutes, T = 18 gives 1,260 and T = 38 gives 7,980.
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