Four different mobile devices make a beep sound after every 30 min, 45 min, 1 h and 1$$\frac{1}{2}$$​ h respectively. All the mobiles beeped together at 10.45 a.m. They will again beep together at:

Correct option is C

Given:

Four different mobile devices beep at intervals of:

30 minutes

45 minutes

1 hour

1 hour 30 minutes (1.5 hours)

They all beeped together at 10:45 a.m. We need to find the next time they will beep together.

Solution:

LCM of 30, 45, 60, and 90:

30 = $$2 \times 3 \times 5$$​​

45 = $$3^2 \times 5$$​​

60 =$$2^2 \times 3 \times 5$$​​

90 = $$2 \times 3^2 \times 5$$​​

LCM = $$2^2 \times 3^2 \times 5 = 4 \times 9 \times 5 = 180 \text{ minutes} =3 \text{ hours}$$​

The mobiles will beep together again 3 hours after 10:45 a.m.:

10:45 a.m. + 3 hours = 1:45 p.m.

Thus, the mobiles will beep together again at 1:45 p.m..