Solve for q 1/(2q)+1/(3q)=5

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

Since ${\displaystyle 2q,3q,1}$ contain both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part ${\displaystyle 2,3,1}$ then find LCM for the variable part ${\displaystyle q^1,q^1}$.

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

Since ${\displaystyle 2}$ has no factors besides ${\displaystyle 1}$ and ${\displaystyle 2}$.

Since ${\displaystyle 3}$ has no factors besides ${\displaystyle 1}$ and ${\displaystyle 3}$.

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

The LCM of ${\displaystyle 2,3,1}$ is the result of multiplying all prime factors the greatest number of times they occur in either number.

Multiply ${\displaystyle 2}$ by ${\displaystyle 3}$.

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

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

The LCM for ${\displaystyle 2q,3q,1}$ is the numeric part ${\displaystyle 6}$ multiplied by the variable part.

Multiply each term in ${\displaystyle \frac{1}{2q}+\frac{1}{3q}=5}$ by ${\displaystyle 6q}$.

Simplify the left side.

Simplify the right side.

Rewrite the equation as ${\displaystyle 30q=5}$.

Divide each term in ${\displaystyle 30q=5}$ by ${\displaystyle 30}$ and simplify.