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The problem presented in the image is about determining when three alarms with different snooze intervals will ring together again.

### Problem details:
- Akash and his parents each set an alarm on their phones for 5:00 a.m.
- The snooze times are 12 minutes, 8 minutes, and 18 minutes, respectively.
- All the alarms rang together at 5:00 a.m.

### Question:
Find the next time their alarms will ring together again.

### Solution approach:
1. We need to find the Least Common Multiple (LCM) of the three snooze times: 12 minutes, 8 minutes, and 18 minutes. This will give us the time after which the alarms will ring together again.

2. **LCM calculation:**
   - Prime factorization of 12: \(12 = 2^2 \times 3\)
   - Prime factorization of 8: \(8 = 2^3\)
   - Prime factorization of 18: \(18 = 2 \times 3^2\)

   The LCM is found by taking the highest powers of all prime factors:
   - Highest power of 2: \(2^3\)
   - Highest power of 3: \(3^2\)

   Therefore, LCM = \(2^3 \times 3^2 = 8 \times 9 = 72\) minutes.

3. The alarms will ring together again 72 minutes after 5:00 a.m.

4. **Final answer:**
   72 minutes after 5:00 a.m. is **6:12 a.m.**

### Conclusion:
The alarms will ring together again at **6:12 a.m.**.

Would you like more details or further clarification? Here are some related questions:

1. How do you find the LCM of larger numbers with more factors?
2. What is the difference between LCM and Greatest Common Divisor (GCD)?
3. Can the LCM method be applied to non-integer numbers?
4. What is the significance of prime factorization in finding the LCM?
5. How can you solve such problems using a calculator?

**Tip:** To quickly find the LCM of two or more numbers, always start by listing their prime factors.

Akash and his parents each set an alarm on their mobile phones for 5:00 a.m. The snooze times were 12 minutes, 8 minutes, and 18 minutes, respectively. All the alarms started ringing at 5:00 a.m. They didn’t turn off the alarms. Find the next time their alarms will ring together again. Show your work.

In this problem, learn how to find the next time three alarms, snoozing at 12, 8, and 18 minutes, will ring together. By calculating the Least Common Multiple (LCM) using prime factorization, students can understand key mathematical concepts. Suitable for Grades 5-7.

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