What is the least common denominator of these two fractions?

Question

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 \( \boxed{18} \).