Since the LCM of 15 and 20 is 60, this means that it will take 60 minutes (1 hour) for the buses to meet at the same time again. So an hour from 8:30 a.m. is 9:30 a.m.
So the buses will meet at 9:30 a.m.
Here's a table to confirm the answer:
Yellow | Blue
-----------------
8:30 | 8:30
8:45 | 8:50
9:00 | 9:10
9:15 | 9:30
9:30 |