Seven. a) When will the bells ring together again if they ring every 18, 16, and 12 hours?

Here's the solution to your questions:

Question Seven

a) To find when the bells will ring together again, we need to find the Least Common Multiple (LCM) of their ringing intervals: 18 hours, 16 hours, and 12 hours.

Step 1: Find the prime factorization of each number.

$$18 = 2 \times 3^2$$ $$16 = 2^4$$ $$12 = 2^2 \times 3$$

Step 2: Calculate the LCM by taking the highest power of each prime factor present.

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