The lowest common denominator of 1/2, 1/3, and 1/4 is:

24
12
6

1 answer

To find the lowest common denominator (LCD) of the fractions \( \frac{1}{2}, \frac{1}{3}, \) and \( \frac{1}{4} \), we need to determine the least common multiple (LCM) of the denominators 2, 3, and 4.

  1. Prime Factorization:

    • \( 2 = 2^1 \)
    • \( 3 = 3^1 \)
    • \( 4 = 2^2 \)
  2. Identify the highest power of each prime factor:

    • For \( 2 \): the highest power is \( 2^2 \) (from 4).
    • For \( 3 \): the highest power is \( 3^1 \) (from 3).
  3. Multiply the highest powers together: \[ \text{LCM} = 2^2 \times 3^1 = 4 \times 3 = 12 \]

Therefore, the lowest common denominator of \( \frac{1}{2}, \frac{1}{3}, \) and \( \frac{1}{4} \) is 12.