Find the least common denominator (LCD). \[ \frac{d}{(5 d-2)(d-7)} ; \frac{6}{(5 d-2)(d+4)} \]

To find the least common denominator (LCD) of the fractions \(\frac{d}{(5 d-2)(d-7)}\) and \(\frac{6}{(5 d-2)(d+4)}\), we first identify the denominators: 1. \( (5d - 2)(d - 7) \) 2. \( (5d - 2)(d + 4) \) Now, we look for the unique factors in both denominators. The first denominator has the factors \( (5d - 2) \) and \( (d - 7) \), while the second has \( (5d - 2) \) and \( (d + 4) \). To create the least common denominator, we take each unique factor at its highest occurrence: - \( (5d - 2) \) appears in both, so we include it once. - \( (d - 7) \) appears in the first denominator. - \( (d + 4) \) appears in the second denominator. Thus, the least common denominator (LCD) is: \[ \text{LCD} = (5d - 2)(d - 7)(d + 4) \]