An electronic device makes a beep after every 60 seconds. Another device makes a beep after 62 seconds.
Question:
An electronic device makes a beep after every 60 seconds. Another device makes a beep after 62 seconds. They beeped together at 10 a.m. At what time will they beep together at the earliest?
Solution:
Beep duration of first device = 60 seconds
Beep duration of second device = 62 seconds
∴ Interval of beeping together = LCM (60, 62)
Prime factorisation:
$60=2^{2} \times 3 \times 5$
$62=2 \times 31$
$\therefore \mathrm{LCM}=2^{2} \times 3 \times 5 \times 31=1860$ seconds $=\frac{1860}{60}=31 \mathrm{~min}$
Hence, they will beep together again at 10 : 31 a.m.