An electronic device makes a beep after every 15 minutes. Another… - Vidyadip

Question

An electronic device makes a beep after every $15$ minutes. Another device makes a beep after every $20$ minutes. They beeped together at $6 a.m.$ At what time will they next beep together?

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Answer

The $LCM$ of the time intervals of the beeps will give the time when the electronic devices will beep together.
$LCM$ of $15$ and $20.$
$\begin{array}{c|c}5&15,20\\\hline3&3,4\\\hline2&1,4\\\hline2&1,2\\\hline&1,1\end{array}$
Required time $5 \times 3 \times 2 \times 2$
$= 60 min$
So, they will beep simultaneously after $60$ min or $1h.$
$\therefore$ They will beep together again at $7:00 a.m.$

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