So would it be to determine the LCD of the above by division of prime numbers 1/9 5/18 three /6 1/90?

To determine the Least Common Denominator (LCD) of the fractions \( \frac{1}{9}, \frac{5}{18}, \frac{3}{6}, \frac{1}{90} \), we need to find the Least Common Multiple (LCM) of their denominators: 9, 18, 6, and 90.

### Steps to find the LCM by prime factorization:

1. **Prime factorization** of the denominators:
   - \( 9 = 3^2 \)
   - \( 18 = 2 \times 3^2 \)
   - \( 6 = 2 \times 3 \)
   - \( 90 = 2 \times 3^2 \times 5 \)

2. **List all the prime factors** involved, taking the highest powers of each:
   - For \( 2 \), the highest power is \( 2^1 \).
   - For \( 3 \), the highest power is \( 3^2 \).
   - For \( 5 \), the highest power is \( 5^1 \).

3. **Multiply these together** to get the LCM:
   \[
   LCM = 2^1 \times 3^2 \times 5^1 = 2 \times 9 \times 5 = 90
   \]

### Therefore, the Least Common Denominator (LCD) of \( \frac{1}{9}, \frac{5}{18}, \frac{3}{6}, \frac{1}{90} \) is **90**.

Would you like me to show how to convert each fraction to have this common denominator?

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Here are 5 relative questions to explore further:

1. How do you convert a fraction to an equivalent fraction with a given denominator?
2. How do you simplify fractions after finding a common denominator?
3. What are some methods to find the LCM of numbers besides prime factorization?
4. How does the Greatest Common Divisor (GCD) differ from the Least Common Multiple (LCM)?
5. How would you find the LCD of improper fractions?

**Tip:** When converting fractions to a common denominator, multiply both the numerator and denominator by the same number to keep the fraction equivalent.

Learn how to find the Least Common Denominator (LCD) of fractions 1/9, 5/18, 3/6, and 1/90 using prime factorization. This step-by-step guide covers important mathematical concepts such as the Least Common Multiple (LCM) and prime factorization. Suitable for students in Grades 6-8.

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