Finding the Least Common Denominator of Rational Expressions
To add fractions that have different denominators, we must first write the
fractions so that they have the same denominator. We call this denominator
the Least Common Denominator or LCD.
Procedure
To Find the Least Common Denominator (LCD) of Rational
Expressions
Step 1 Factor each denominator.
Step 2 For each factor, list it the greatest number of times it appears
in any factorization.
Step 3 Write the product of the factors in the list.
Example 1
Find the LCD:
Solution
Step 1 Factor each denominator.

x^{2} + x  6 = (x + 3)(x
 2)
x^{2}  x  2 = (x + 1)(x  2) 
Step 2 For each factor, list it the greatest
number of times it appears in any
factorization.

x + 3, x  2, x + 1 
Step 3 Write the product of the
factors in the list.

(x + 3)(x  2)(x + 1) 
So, the LCD is (x + 3)(x  2)(x + 1). 

