Find the LCD of Rational Expressions
Find the LCD of x
9x2y2 and 5y
6x2y3z
To add or subtract fractions, each fraction must have the same denominator. This is true for
rational expressions as well: If two rational expressions do not have common denominators in an
addition or subtraction problem, then we may need to rewrite the expressions by using the least
common denominator (LCD).
The following steps can be used to find the LCD of rational expressions:
STEP 1: Factor each denominator into the product of its lowest terms, and express any repeating
factors as powers.
9x2y2, written in its lowest terms will be 3*3*x*x*y*y or 32x2y2.
6x2y3z, written in its lowest terms will be 3*2*x*x*y*y*y*z or 3*2x2y3z.
STEP 2: List all the different factors that appear for each denominator. If a factor is common for
any of the denominators, only list that factor to the highest power that it appears.
The factors that appear in each denominator are 2, 3, x, y and z.
STEP 3: The product of the factors listed in Step 2 will be the LCD.
The LCD is 2*32*x2*y3*z = 18x2y3z.
Example 1: Find the LCD of 1
x and 1
y
x is already written in its lowest term.
y is already written in its lowest term.
Therefore the LCD is x*y= xy.
Example 2: Find the LCD of 2
x2+6x+9 and 2
3x+9
