To solve this problem, we need to find the least common multiple (LCM) of the intervals at which the bells toll, which are 6, 7, 8, 9, and 12 seconds.

Step 1: Prime factorize the numbers
6 = 2 * 3
7 = 7
8 = 2^3
9 = 3^2
12 = 2^2 * 3

Step 2: Find the LCM
The LCM is found by multiplying the highest power of all prime numbers obtained.
So, LCM = 2^3 * 3^2 * 7 = 8 * 9 * 7 = 504 seconds

This means that all bells will toll together every 504 seconds.

Step 3: Convert the LCM to minutes
504 seconds = 504/60 = 8.4 minutes

Step 4: Find how many times the bells toll together in one hour
1 hour = 60 minutes
So, the bells will toll together 60/8.4 = 7.14 times

Since the bells cannot toll a fraction of a time, we round down to the nearest whole number.

So, the bells will toll together 7 times in one hour.

Note: This includes the initial toll at the start of the hour.

Question

To solve this problem, we need to find the least common multiple (LCM) of the intervals at which the bells toll, which are 6, 7, 8, 9, and 12 seconds.

Step 1: Prime factorize the numbers
6 = 2 * 3
7 = 7
8 = 2^3
9 = 3^2
12 = 2^2 * 3

Step 2: Find the LCM
The LCM is found by multiplying the highest power of all prime numbers obtained.
So, LCM = 2^3 * 3^2 * 7 = 8 * 9 * 7 = 504 seconds

This means that all bells will toll together every 504 seconds.

Step 3: Convert the LCM to minutes
504 seconds = 504/60 = 8.4 minutes

Step 4: Find how many times the bells toll together in one hour
1 hour = 60 minutes
So, the bells will toll together 60/8.4 = 7.14 times

Since the bells cannot toll a fraction of a time, we round down to the nearest whole number.

So, the bells will toll together 7 times in one hour.

Note: This includes the initial toll at the start of the hour.

Knowee AI · Accepted Answer

To solve this problem, we need to find the least common multiple (LCM) of the intervals at which the bells toll, which are 6, 7, 8, 9, and 12 seconds.

Step 1: Prime factorize the numbers
6 = 2 * 3
7 = 7
8 = 2^3
9 = 3^2
12 = 2^2 * 3

Step 2: Find the LCM
The LCM is found by multiplying the highest power of all prime numbers obtained.
So, LCM = 2^3 * 3^2 * 7 = 8 * 9 * 7 = 504 seconds

This means that all bells will toll together every 504 seconds.

Step 3: Convert the LCM to minutes
504 seconds = 504/60 = 8.4 minutes

Step 4: Find how many times the bells toll together in one hour
1 hour = 60 minutes
So, the bells will toll together 60/8.4 = 7.14 times

Since the bells cannot toll a fraction of a time, we round down to the nearest whole number.

So, the bells will toll together 7 times in one hour.

Note: This includes the initial toll at the start of the hour.

Five bells begin to toll together and toll respectively at intervals of 6, 7, 8, 9 and 12 seconds. How many times will they toll together in one hour?

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