An electronic device makes a beep after every 60 seconds. Another device makes a beep after 62 seconds.

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.