The correct answer is option (C):
7
To solve this problem, we need to find the least common multiple (LCM) of the intervals at which the bells toll (6, 7, 8, 9, and 12 seconds). The LCM represents the time it takes for all the bells to toll together again.
First, let's find the prime factorization of each number:
* 6 = 2 x 3
* 7 = 7
* 8 = 2 x 2 x 2 = 2^3
* 9 = 3 x 3 = 3^2
* 12 = 2 x 2 x 3 = 2^2 x 3
Now, to find the LCM, we take the highest power of each prime factor that appears in any of the factorizations:
* 2^3 = 8
* 3^2 = 9
* 7 = 7
Multiply these together: 8 x 9 x 7 = 504 seconds.
This means the bells toll together every 504 seconds.
Next, we need to determine how many times they toll together in one hour. One hour is equal to 60 minutes, and one minute is equal to 60 seconds. So, one hour is equal to 60 x 60 = 3600 seconds.
Now, divide the total time (3600 seconds) by the time interval between the tolls (504 seconds):
3600 / 504 = 7.1428...
Since we're asked how many times they toll together *excluding* the initial toll, we only consider the full intervals. The division gives us approximately 7.14, meaning the bells toll together 7 times in the hour, plus the initial toll. The question requests the number of times in the hour, excluding the initial one, thus the correct answer is 7.