Five bells in a church toll at interval of 12 seconds, 15 seconds, 20 seconds, 25 seconds and 45 seconds respectively. If all of them toll at 5 am. What time next, they will toll together?

Options

A. 5.10 am
B. 5.12am
C. 5.15am
D. 5.20am

Explanation

To solve the problem of when the five bells will toll together again after tolling at 5 am, we need to find the least common multiple (LCM) of the intervals at which they toll: 12 seconds, 15 seconds, 20 seconds, 25 seconds, and 45 seconds.

### Step-by-Step Solution:

**Step 1: List the intervals of the bells.**
- The intervals are: 12 seconds, 15 seconds, 20 seconds, 25 seconds, and 45 seconds.

**Step 2: Find the prime factorization of each interval.**
- 12 = 2^2 * 3^1
- 15 = 3^1 * 5^1
- 20 = 2^2 * 5^1
- 25 = 5^2
- 45 = 3^2 * 5^1

**Step 3: Identify the highest power of each prime factor.**
- For 2: The highest power is 2^2 (from 12 and 20).
- For 3: The highest power is 3^2 (from 45).
- For 5: The highest power is 5^2 (from 25).

**Step 4: Calculate the LCM using the highest powers.**
- LCM = 2^2 * 3^2 * 5^2
- LCM = 4 * 9 * 25

**Step 5: Perform the multiplication step-by-step.**
- First, calculate 4 * 9 = 36.
- Then, calculate 36 * 25 = 900.

**Step 6: Convert seconds into minutes.**
- 900 seconds ÷ 60 seconds/minute = 15 minutes.

**Step 7: Determine the next time they will toll together.**
- Since they toll together at 5 am, adding 15 minutes gives us:
- 5:00 am + 15 minutes = 5:15 am.

### Final Answer:
The next time all five bells will toll together is at **5:15 am**.

---