Question

What is the least common denominator of these two fractions?
5/9 and 1/2

Answer 1

To find the least common denominator (LCD) of the fractions \( \frac{5}{9} \) and \( \frac{1}{2} \), we need to determine the least common multiple (LCM) of the denominators, which are 9 and 2.

1. **Identify the denominators**: The denominators are 9 and 2.
2. **Find the prime factorization**:
- The prime factorization of 9 is \( 3^2 \).
- The prime factorization of 2 is \( 2^1 \).

3. **Determine the LCM**:
- For each prime factor, take the highest power that appears in either factorization:
- For prime factor 2: the highest power is \( 2^1 \).
- For prime factor 3: the highest power is \( 3^2 \).

4. **Multiply these together to find the LCM**:
\[
\text{LCM} = 2^1 \times 3^2 = 2 \times 9 = 18
\]

Thus, the least common denominator of \( \frac{5}{9} \) and \( \frac{1}{2} \) is \( \boxed{18} \).