Question

What is the least common denominator of these two fractions?

2/5 and 1/6

Answer 1

To find the least common denominator (LCD) of the fractions \( \frac{2}{5} \) and \( \frac{1}{6} \), we first need to determine the denominators of the fractions, which are 5 and 6.

The next step is to find the least common multiple (LCM) of these two numbers.

1. **Identify the prime factorization:**
- The prime factorization of 5 is \( 5^1 \).
- The prime factorization of 6 is \( 2^1 \times 3^1 \).

2. **Find the LCM by taking the highest power of each prime factor:**
- The primes in consideration are 2, 3, and 5.
- The highest power of 2 is \( 2^1 \).
- The highest power of 3 is \( 3^1 \).
- The highest power of 5 is \( 5^1 \).

3. **Calculate the LCM:**
\[
\text{LCM} = 2^1 \times 3^1 \times 5^1 = 2 \times 3 \times 5
\]
\[
2 \times 3 = 6
\]
\[
6 \times 5 = 30
\]

Thus, the least common denominator (LCD) of \( \frac{2}{5} \) and \( \frac{1}{6} \) is \( \boxed{30} \).