Answer
LCD = $900n^2p$
$\frac{35m}{900n^2p}$
$\frac{24n^3}{900n^2p}$
Work Step by Step
The first thing we want to do is to factor each denominator completely:
$\frac{7m}{3 • 3 • 2 • 2 • 5 • n^2 • p}$
$\frac{4n}{3 • 5 • 5 • 2 • p}$
Next, we want to take the highest power of each factor in the denominator:
LCD = $3^2 • 2^2 • 5^2 •n^2 • p$
Multiply the factors out:
LCD = $9 • 4 • 25 •n^2 • p$
Simplify:
LCD = $900n^2p$
Now that we have the least common denominator, we multiply the numerators of each fraction with the factors it is missing in the denominator:
$\frac{7m • 5}{900n^2p}$
$\frac{4n • 3 • 2 • n^2}{900n^2p}$
Simplify the fractions:
$\frac{35m}{900n^2p}$
$\frac{24n^3}{900n^2p}$
