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Let's solve the problem of finding the Least Common Multiple (LCM) for each of the given pairs of numbers:

### 1. **LCM of 4 and 9:**
- Prime factors of 4: \( 2^2 \)
- Prime factors of 9: \( 3^2 \)

To find the LCM, take the highest powers of all prime factors: 
- \( LCM = 2^2 \times 3^2 = 4 \times 9 = 36 \)

So, the **LCM of 4 and 9 is 36**.

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### 2. **LCM of 6 and 8:**
- Prime factors of 6: \( 2 \times 3 \)
- Prime factors of 8: \( 2^3 \)

To find the LCM, take the highest powers of all prime factors:
- \( LCM = 2^3 \times 3 = 8 \times 3 = 24 \)

So, the **LCM of 6 and 8 is 24**.

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### 3. **LCM of 10 and 12:**
- Prime factors of 10: \( 2 \times 5 \)
- Prime factors of 12: \( 2^2 \times 3 \)

To find the LCM, take the highest powers of all prime factors:
- \( LCM = 2^2 \times 3 \times 5 = 4 \times 3 \times 5 = 60 \)

So, the **LCM of 10 and 12 is 60**.

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### Relative questions

Find the LCM of the following numbers: 4 and 9, 6 and 8, 10 and 12.

Learn how to find the Least Common Multiple (LCM) of 4 and 9, 6 and 8, 10 and 12. This problem covers prime factorization and the LCM theorem. Suitable for students in Grades 6-8.

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