Final answer:
The alarm clocks will ring together at 3am after finding the Least Common Multiple of their ringing intervals, which is 60 minutes.
Step-by-step explanation:
The question asks about the next time two alarm clocks with different ringing intervals will ring together after initially ringing at 2am.
Facts given: The first clock rings every 20 minutes and the second clock rings every 30 minutes. Both clocks ring together at 2am.
Keywords: alarm clocks, rings, minutes, same time.
Solution: To solve this problem, find the Least Common Multiple (LCM) of the two intervals (20 and 30 minutes). The LCM of 20 and 30 is 60 minutes, which means the clocks will ring together every 60 minutes, or every hour after they first rang together at 2am. The clocks will next ring together at 3am.
Answer: The alarm clocks will ring together at 3am.