Final answer:
The clocks will chime together two times from 2pm to 9pm, excluding the initial chime at 2pm.
Step-by-step explanation:
The subject of this question is Mathematics, particularly focusing on the least common multiple and time intervals. The grade level of the question is likely Middle School. To solve this problem, we need to find the least common multiple (LCM) of the time intervals at which each clock chimes: 10, 12, and 18 minutes. The LCM of 10, 12, and 18 is 180 minutes, which means the three clocks will chime together every 180 minutes, or every 3 hours.
From 2pm to 9pm is a 7-hour span. Since the clocks just chimed together at 2pm, they will chime together again at 5pm and 8pm. Therefore, within this timeframe, excluding the initial chime at 2pm, the clocks will chime together two times.