Question

What is the least common denominator of these two fractions?
1/6 and 5/8

Answer 1

To find the least common denominator (LCD) of the fractions \( \frac{1}{6} \) and \( \frac{5}{8} \), we need to determine the least common multiple (LCM) of the denominators 6 and 8.

First, we find the prime factorizations of the denominators:

- The prime factorization of \( 6 \) is:
\[
6 = 2 \times 3
\]

- The prime factorization of \( 8 \) is:
\[
8 = 2^3
\]

Next, we take the highest power of each prime factor present in these factorizations:

- For the prime \( 2 \): the highest power is \( 2^3 \) (from 8).
- For the prime \( 3 \): the highest power is \( 3^1 \) (from 6).

Now, we find the LCM by multiplying these highest powers together:

\[
\text{LCM} = 2^3 \times 3^1 = 8 \times 3 = 24
\]

Thus, the least common denominator of \( \frac{1}{6} \) and \( \frac{5}{8} \) is \( \boxed{24} \).