Question

What is the least common denominator of these two fractions?
2/7 and 1/4

Answer 1

Hi

Answer 2

Are you cheating?

Answer 3

To find the least common denominator (LCD) of the fractions \( \frac{2}{7} \) and \( \frac{1}{4} \), we need to determine the least common multiple (LCM) of the denominators 7 and 4.

1. The prime factorization of 7 is \( 7^1 \).
2. The prime factorization of 4 is \( 2^2 \).

To find the LCM, we take each prime factor raised to the highest power that appears in the factorizations:

- For the prime number 2, the highest power in the factorizations is \( 2^2 \).
- For the prime number 7, the highest power is \( 7^1 \).

Now, we multiply these together to find the LCM:

\[
\text{LCM} = 2^2 \times 7^1 = 4 \times 7 = 28.
\]

Thus, the least common denominator of the fractions \( \frac{2}{7} \) and \( \frac{1}{4} \) is \( \boxed{28} \).