Solve for q 3/p+1/q=16/(5p)

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

Since ${\displaystyle q,5p,p}$ contain both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part ${\displaystyle 1,5,1}$ then find LCM for the variable part ${\displaystyle q^1,p^1,p^1}$.

The LCM is the smallest positive number that all of the numbers divide into evenly.

The number ${\displaystyle 1}$ is not a prime number because it only has one positive factor, which is itself.

Since ${\displaystyle 5}$ has no factors besides ${\displaystyle 1}$ and ${\displaystyle 5}$.

The number ${\displaystyle 1}$ is not a prime number because it only has one positive factor, which is itself.

The LCM of ${\displaystyle 1,5,1}$ is the result of multiplying all prime factors the greatest number of times they occur in either number.

The factor for ${\displaystyle q^1}$ is ${\displaystyle q}$ itself.

The factor for ${\displaystyle p^1}$ is ${\displaystyle p}$ itself.

The LCM of ${\displaystyle q^1,p^1,p^1}$ is the result of multiplying all prime factors the greatest number of times they occur in either term.

Multiply ${\displaystyle q}$ by ${\displaystyle p}$.

The LCM for ${\displaystyle q,5p,p}$ is the numeric part ${\displaystyle 5}$ multiplied by the variable part.

Multiply each term in ${\displaystyle \frac{1}{q}=\frac{16}{5p}-\frac{3}{p}}$ by ${\displaystyle 5qp}$.

Simplify the left side.

Simplify the right side.