, ,

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

Since contain both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part then find LCM for the variable part .

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

1. List the prime factors of each number.

2. Multiply each factor the greatest number of times it occurs in either number.

Since has no factors besides and .

is a prime number

Since has no factors besides and .

is a prime number

has factors of and .

The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either number.

Multiply by .

Multiply by .

The factor for is itself.

occurs time.

The factors for are , which is multiplied by each other times.

occurs times.

The factor for is itself.

occurs time.

The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either term.

Multiply by .

The LCM for is the numeric part multiplied by the variable part.

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