What is the least common denominator of the exponents?

The Least Common Denominator (also called LCD) is very important to working with rational expressions. The process we use to find the LCD of the exponents is based on the process used to find the LCD of intergers. For instance, to find the LCD of 8 and 6 you need:

1. Consider multiples of the larger number
8, 16, 24,...

2. 24 is the first multiple of 8 that is also divisible by 6

3. Then 24 is our Solution.

To answer the question regarding expressions with exponents let's take an example:

Find the LCD of [tex]4x^{2}y^{5} \ and \ 6x^{4}y^{3}z^{6}[/tex]:

1. 12 is the LCD of 4 and 6

2. Use all variables with highest exponents on each variable, then [tex]x^{4}y^{5}z^{6}[/tex]

3. Finally, solutions is: [tex]12x^{4}y^{5}z^{6}[/tex]