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 1

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:

$$\begin{gathered} \begin{array}{l}5\overline{)15,20}\\ 3\overline{)3,4}\\ 2\overline{)1,4}\\ 2\overline{)1,2}\end{array} \\ \overline{)1,1} \end{gathered}$$

Required time = 5 × 3 × 2 × 2
= 60 min
So, they will beep simultaneously after 60 min or 1 h.

∴ They will beep together again at 7:00 a.m.