Find the LCD 1/(3x) , 4/(5x^2) , (2+x)/(6x)

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

Since ${\displaystyle 3x,5x^2,6x}$ contains both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part ${\displaystyle 3,5,6}$ then find LCM for the variable part ${\displaystyle x^1,x^2,x^1}$.

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

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

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

${\displaystyle 6}$ has factors of ${\displaystyle 2}$ and ${\displaystyle 3}$.

The LCM of ${\displaystyle 3,5,6}$ is the result of multiplying all prime factors the greatest number of times they occur in either number.

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

The factors for ${\displaystyle x^2}$ are ${\displaystyle x\cdot x}$, which is ${\displaystyle x}$ multiplied by each other ${\displaystyle 2}$ times.

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

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

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