https://file.aiquickdraw.com/mathbot/file/1727343183689k1ca2og4.jpg

The first question from the image reads:

**1. Three bells ring at intervals of 10, 15, and 20 minutes respectively. If they ring together at 12 o'clock, at what time will they ring together next?**

To solve this, we need to find the Least Common Multiple (LCM) of the intervals (10, 15, and 20 minutes). The LCM will give us the time after which the bells will ring together again.

Let's calculate the LCM of 10, 15, and 20.

1. **Prime factorization**:
   - 10 = 2 × 5
   - 15 = 3 × 5
   - 20 = 2² × 5

2. **LCM**: To find the LCM, we take the highest powers of all prime factors:
   - 2² (from 20)
   - 3 (from 15)
   - 5 (common in all)

   So, LCM = \( 2^2 \times 3 \times 5 = 4 \times 3 \times 5 = 60 \).

Thus, the bells will ring together after 60 minutes.

### Conclusion:
If the bells ring together at 12 o'clock, they will ring together next at **1:00 PM**.

Would you like any further details on this or other questions? Here are some related questions to explore:

1. How do you calculate the LCM of any set of numbers?
2. What is the importance of prime factorization in finding the LCM?
3. Can you explain how to find the greatest common divisor (GCD) using prime factorization?
4. How often would the bells ring together in a 12-hour period?
5. What if the bells rang at non-integer intervals like 7.5 minutes?

**Tip:** Always break down numbers into their prime factors to make LCM and GCD calculations easier.

Three bells ring at intervals of 10, 15, and 20 minutes respectively. If they ring together at 12 o'clock, at what time will they ring together next?

Learn how to find the time when three bells ring together again after 12 o'clock using the Least Common Multiple (LCM) method. This problem involves prime factorization and is suitable for Grade 5 students.

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