1. The problem is to find the least common denominator (LCD) from the given options: 40xy2, 40xy3, 40x2y, 40x3y. 2. The LCD is the smallest expression that contains all the factors of the denominators involved. 3. Let's analyze each option: - Option A: $40xy^2$ means $40 \times x \times y^2$ - Option B: $40xy^3$ means $40 \times x \times y^3$ - Option C: $40x^2y$ means $40 \times x^2 \times y$ - Option D: $40x^3y$ means $40 \times x^3 \times y$ 4. To find the LCD, we take the highest powers of each variable present: - For $x$, the highest power is $x^3$ (from Option D) - For $y$, the highest power is $y^3$ (from Option B) - The constant factor 40 is common in all options 5. Therefore, the LCD is: $$40x^3y^3$$ 6. Among the options, none exactly matches $40x^3y^3$, but the closest is Option D: $40x^3y$, which has the highest power of $x$ but not $y$. 7. Since the problem asks to find the LCD from the options given, and none has $y^3$, the LCD must include the highest powers of both variables, so the LCD is $40x^3y^3$ (not listed). Final answer: The least common denominator is $40x^3y^3$ (not among the options).