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The question asks to find the least common denominator (LCD) for the fractions \( \frac{4}{9}, \frac{11}{12}, \text{ and } \frac{28}{18} \).

### Step 1: Factor the denominators
- The denominator of \( \frac{4}{9} \) is 9. Factor of 9: \( 9 = 3^2 \)
- The denominator of \( \frac{11}{12} \) is 12. Factor of 12: \( 12 = 2^2 \times 3 \)
- The denominator of \( \frac{28}{18} \) is 18. Factor of 18: \( 18 = 2 \times 3^2 \)

### Step 2: Find the least common denominator (LCD)
To find the LCD, take the highest powers of each prime factor:
- For 2: The highest power is \( 2^2 \) (from 12).
- For 3: The highest power is \( 3^2 \) (from both 9 and 18).

Thus, the LCD is:
\[
\text{LCD} = 2^2 \times 3^2 = 4 \times 9 = 36
\]

### Answer:
The least common denominator is **36**.

Would you like further details or have any questions?

Here are 5 related questions to expand on this topic:
1. How do you find the least common denominator for multiple fractions?
2. What are the steps to convert fractions with different denominators to equivalent fractions with the LCD?
3. How does factoring help in finding the least common denominator?
4. Can the least common multiple (LCM) of the denominators always be used as the LCD?
5. How does the LCD simplify addition or subtraction of fractions?

**Tip:** When finding the LCD, always look for the highest powers of prime factors in the denominators.

Which is the least common denominator for the fractions 4/9, 11/12, and 28/18?

Learn how to find the least common denominator for the fractions 4/9, 11/12, and 28/18 using prime factorization. This problem demonstrates how to break down denominators into prime factors and select the highest powers to calculate the LCD. Suitable for students in Grades 6-8.

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