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?
✓
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 × 3 × 2 × 2
= 60 min
So, they will beep simultaneously after 60 min or 1h.
$\therefore$ They will beep together again at 7:00 a.m.
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 × 3 × 2 × 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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