Four different devices beep after every half hour, 60 min, 1 and half hours, and 135 min respectively. All the devices beeped together at 12 noon. They will beep together again at:
12 midnight
6 AM
9 AM
7.30 AM
Interval after which the devices will beep together = (L.C.M. of 30, 60, 90, 105) min.
= 1260 min. = 21 hrs.
So, the devices will again beep together 21 hrs. after 12 noon i.e., at 9 a.m.