Answer:

Six bells commence tolling together and toll at intervals of 2, 4, 6, 8, 10, and 12 seconds respectively. In 30 minutes, they toll together 16 times. The concept used is Least common multiplication. But we have to add 1 because at the start all bells will be rung once a time after that they ring 15 times.

Step-by-step explanation:

• Sure, I can help you with that.

The number of times the bells will toll together is one more than the number of gaps between the tolls. So we need to find the greatest common factor of 2, 4, 6, 8, 10, and 12.

• The prime factorization of these numbers is:

* 2 = 2

* 4 = 2^2

* 6 = 2 * 3

* 8 = 2^3

* 10 = 2 * 5

* 12 = 2^2 * 3

The greatest common factor is 2^2 = 4.

So the bells will toll together 4 + 1 = 5 times in 30 minutes.

Here is the step-by-step explanation:

1. Find the prime factorization of the 6 numbers: 2, 4, 6, 8, 10, and 12.

2. Find the highest power of each prime number in the prime factorization. The highest power of 2 is 2^2, the highest power of 3 is 1, and the highest power of 5 is 0.

3. The greatest common factor is the product of the highest powers of the prime numbers. The greatest common factor is 2^2 = 4.

4. Add 1 to the greatest common factor to find the number of times the bells will toll together. The number of times the bells will toll together is 4 + 1 = 5 times.

• I hope this helps! Let me know if you have any other questions.