Find the LCD of 5/18x^2y^3,-3/24x^4y^5
To find the least common denominator (LCD) of the fractions 5/18x^2y^3 and -3/24x^4y^5, we need to determine the smallest expression that is divisible by all the denominators.
First, let's break down the denominators and identify their prime factors:
- The denominator of 5/18x^2y^3 is 18x^2y^3, which can be written as 2 * 3^2 * x^2 * y^3.
- The denominator of -3/24x^4y^5 is 24x^4y^5, which can be written as 2^3 * 3 * x^4 * y^5.
To find the LCD, we need to take the highest power of each prime factor that appears in either denominator:
- The LCD should have a factor of 2^3, which covers both denominators.
- Since the first denominator includes 3^2 and the second denominator includes 3, the LCD should have the factor 3^2.
- The first denominator includes x^2, while the second denominator includes x^4. We need the highest power of x, so the LCD should include x^4.
- Similarly, the first denominator includes y^3, while the second denominator includes y^5. We need the highest power of y, so the LCD should include y^5.
Now, we can combine these factors to get the LCD:
2^3 * 3^2 * x^4 * y^5
Therefore, the LCD of 5/18x^2y^3 and -3/24x^4y^5 is 72x^4y^5.