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