Question

There are three bells that ring at different intervals. The first bell rings every 6 minutes, the second

bell rings every 7 minutes, The third bell rings 9 minutes. If all the bells ring together at noon, at what
time will they next all ring together?

Answer 1

To determine the next time all three bells ring together, calculate the least common multiple (LCM) of 6, 7, and 9, which is 126 minutes. Thus, the bells will next ring together at 2:06 PM.

Step-by-step explanation:

To find the next time when all the bells will ring together, we need to determine the least common multiple (LCM) of the intervals at which the bells ring. The first bell rings every 6 minutes, the second bell rings every 7 minutes, and the third bell rings every 9 minutes. The LCM of 6, 7, and 9 is the smallest number that is a multiple of all three numbers.

Calculating the LCM of 6, 7, and 9:

• Prime factorization of 6 = 2 × 3
• Prime factorization of 7 = 7 (since 7 is a prime number)
• Prime factorization of 9 = 3 × 3

LCM = 2 × 3 × 3 × 7 = 126

Therefore, the bells will all ring together again 126 minutes after noon. Since there are 60 minutes in an hour, this is 2 hours and 6 minutes later. So, the next time all the bells will ring together is at 2:06 PM.

Answer 2

2:06

Step-by-step explanation:

You just need to find the Least Common Multiple of the 3 numbers. In this case it was 126 which if those are minutes that would mean 2 hours and 6 minutes.