Find the LCD 5/(9m^2n) and 5/(16mn^3)

$\frac{5}{9 m^{2} n}$ and $\frac{5}{16 m n^{3}}$

To find the LCD of a set of numbers $(\frac{5}{9 m^{2} n}, \frac{5}{16 m n^{3}})$ , find the LCM of the denominators.

$LCM (9 m^{2} n, 16 m n^{3})$

Calculate the LCM of first two denominators in the list, $9 m^{2} n$ and $16 m n^{3}$ .

For each instance of a variable included in the terms, compare the power of the variable in term one with the power of the variable in term two. Return the variable with the larger exponent.

First Term: $9 m^{2} n$

Second Term: $16 m n^{3}$

For variable $m$ , $m^{2}$ has a greater power than $m^{1}$ , so keep $m^{2}$ .

$m^{2}$

For variable $n$ , $n^{3}$ has a greater power than $n^{1}$ , so keep $n^{3}$ .

$n^{3}$

Find the values of the numerical part of each term. Select the largest one, which in this case is $16$ . Multiply them together to get the current total. In this case, the current total is $144$ .

Current Total = $144$