At a Bhopal bus depot, buses on route A leave every 35 minutes, route B every 45 minutes and route C every 63 minutes. All three leave together at 5:30 am.
At what time will all three next leave together?

LCM(35, 45, 63): $35=5\times 7,45=3^2\times$ 5 and $63=3^2\times$ 7, so LCM = $3^2\times 5\times 7=315$ minutes = 5 hours 15 minutes. 5:30 am + 5 h 15 min = 10:45 am. Adding the intervals (35 + 45 + 63 = 143 min) gives 7:53 am; using only the longest interval gives 6:33 am; doubling the LCM gives 4:00 pm.