Answer
$72x^{4}y^{5}$
Work Step by Step
We are given the denominators $18x^{2}y^{3}$ and $24x^{4}y^{5}$.
In order to find the least common denominator, we must factor each denominator.
$18x^{2}y^{3}=3\times3\times2\times x^{2}\times y^{2}=3^{2}\times2\times x^{2}\times y^{2}$
$24x^{4}y^{5}=3\times2\times2\times2\times x^{4}\times y^{5}=3\times2^{3}\times x^{4}\times y^{5}$
Next, we multiply together all distinct factors from each denominator, with each factor raised to the greatest power that occurs in any denominator.
$LCD=3^{2}\times2^{3}\times x^{4}\times y^{5}=9\times8\times x^{4}\times y^{5}=72x^{4}y^{5}$
