Find the least common denominator of \( \frac{3}{2 x-8} \) and \( \frac{2 x}{5 x-20} \). \[ \square \]

To find the least common denominator (LCD) of the fractions \( \frac{3}{2x-8} \) and \( \frac{2x}{5x-20} \), we first factor the denominators. The first denominator: \[ 2x - 8 = 2(x - 4) \] The second denominator: \[ 5x - 20 = 5(x - 4) \] Next, we can observe that both denominators share a common factor of \( (x - 4) \). Now we can express the denominators fully: - First fraction: \( 2(x - 4) \) - Second fraction: \( 5(x - 4) \) To find the LCD, we take the highest power of each factor present in the denominators: - From \( 2(x - 4) \), we have \( 2 \) and \( (x - 4) \). - From \( 5(x - 4) \), we have \( 5 \) and \( (x - 4) \). Thus, the LCD is: \[ \text{LCD} = 2 \times 5 \times (x - 4) = 10(x - 4) \] So, the least common denominator of \( \frac{3}{2 x-8} \) and \( \frac{2 x}{5 x-20} \) is: \[ \boxed{10(x - 4)} \]