Find the least common denominator of \( \frac{2}{7 x-14} \) and \( \frac{x}{3 x-6} \) \( \square \)

To find the least common denominator (LCD) of the fractions \( \frac{2}{7x-14} \) and \( \frac{x}{3x-6} \), we first need to factor the denominators. The first denominator \( 7x - 14 \) can be factored as: \[ 7(x - 2) \] The second denominator \( 3x - 6 \) can be factored as: \[ 3(x - 2) \] Now, we identify the factors from both denominators: - From \( 7(x-2) \), we have \( 7 \) and \( (x-2) \). - From \( 3(x-2) \), we have \( 3 \) and also \( (x-2) \). To find the LCD, we take the highest power of each unique factor: - The highest power of \( 7 \) is \( 7^1 \). - The highest power of \( 3 \) is \( 3^1 \). - The factor \( (x - 2) \) appears in both denominators, so we take \( (x - 2)^1 \). Thus, the least common denominator is: \[ LCD = 7 \times 3 \times (x - 2) = 21(x - 2) \] So the least common denominator of \( \frac{2}{7x-14} \) and \( \frac{x}{3x-6} \) is \( 21(x - 2) \).