Solve for x 1/x+1/(5x)=1/(15a)

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

Since ${\displaystyle x,5x,15a}$ contain both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part ${\displaystyle 1,5,15}$ then find LCM for the variable part ${\displaystyle x^1,x^1,a^1}$.

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 ${\displaystyle 5}$.

${\displaystyle 15}$ has factors of ${\displaystyle 3}$ and ${\displaystyle 5}$.

Multiply ${\displaystyle 3}$ by ${\displaystyle 5}$.

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

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

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

Multiply ${\displaystyle x}$ by ${\displaystyle a}$.

The LCM for ${\displaystyle x,5x,15a}$ is the numeric part ${\displaystyle 15}$ multiplied by the variable part.

Multiply each term in ${\displaystyle \frac{1}{x}+\frac{1}{5x}=\frac{1}{15a}}$ by ${\displaystyle 15xa}$.

Simplify the left side.

Simplify the right side.