A wall clock chimes every 25 minutes and a wristwatch alarm sounds every 40 minutes. Both go off together at 8:00 a.m.
How many times will they go off together during the next 12 hours?

LCM(25, 40): $25=5^2$ and $40=2^3\times$ 5, so LCM = $2^3\times 5^2=200$ minutes = 3 h 20 min. Starting from 8:00 a.m. they coincide at 11:20 a.m., 2:40 p.m. and 6:00 p.m. - 3 times, since the next would be 9:20 p.m., beyond the 12-hour window. Answering 4 counts the 8:00 a.m. start as well; 144 uses the HCF of 5 minutes; 18 uses only the 40-minute interval.