What is the least common denominator of these two fractions?

2/7 and 1/4

3 answers

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 \( \boxed{28} \).

Hi
Are you cheating?