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The problem asks to compare two fractions: \( \frac{4}{6} \) and \( \frac{4}{8} \), using the least common denominator (LCD), also known as the least common multiple (LCM) of the denominators.

### Step-by-step solution:

1. **Find the LCM of 6 and 8:**
   - The prime factors of 6 are \( 2 \times 3 \).
   - The prime factors of 8 are \( 2^3 \).
   - The LCM is found by taking the highest power of all primes that appear in the factorizations. Here, that would be \( 2^3 \times 3 = 24 \).
   - So, the LCM of 6 and 8 is 24.

2. **Convert the fractions to have the same denominator (24):**
   - For \( \frac{4}{6} \), multiply both numerator and denominator by 4 to get: 
     \[
     \frac{4}{6} = \frac{16}{24}
     \]
   - For \( \frac{4}{8} \), multiply both numerator and denominator by 3 to get: 
     \[
     \frac{4}{8} = \frac{12}{24}
     \]

3. **Compare the two fractions:**
   - Now, you are comparing \( \frac{16}{24} \) and \( \frac{12}{24} \).
   - Clearly, \( \frac{16}{24} > \frac{12}{24} \).

### Conclusion:
The correct inequality is:
\[
\frac{4}{6} > \frac{4}{8}
\]

Would you like more details on any part of the explanation?

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Here are five relative questions to expand this concept:
1. How do you find the least common multiple (LCM) of any two numbers?
2. What other methods can be used to compare fractions without finding the LCM?
3. Can you explain why reducing fractions helps in comparisons?
4. How do you convert improper fractions to mixed numbers?
5. How do you solve word problems that involve comparing fractions?

**Tip:** Always simplify fractions before comparing them—it makes the process faster and easier.

Compare the fractions 4/6 and 4/8 using the LCM. Enter the correct inequality in the box.

Learn how to compare the fractions 4/6 and 4/8 using the least common multiple (LCM) of the denominators. This step-by-step solution shows how to convert fractions to a common denominator and find the correct inequality. Suitable for students in Grades 4-6.

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