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 four steps to find the LCM. Find LCM for the numeric, variable, and compound variable parts. Then, multiply them all together.

Steps to find the LCM for are:

1. Find the LCM for the numeric part .

2. Find the LCM for the variable part .

3. Find the LCM for the compound variable part .

4. Multiply each LCM together.

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.

The number is not a prime number because it only has one positive factor, which is itself.

Not prime

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

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.

The factor for is itself.

occurs time.

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

The Least Common Multiple of some numbers is the smallest number that the numbers are factors of.

Multiply each term in by in order to remove all the denominators from the equation.

Simplify .

Simplify each term.

Cancel the common factor of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Cancel the common factor of .

Move the leading negative in into the numerator.

Cancel the common factor.

Rewrite the expression.

Apply the distributive property.

Rewrite as .

Multiply by .

Simplify by adding terms.

Subtract from .

Add and .

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Since , the equation will always be true for any value of .

All real numbers

The result can be shown in multiple forms.

All real numbers

Interval Notation:

Solve for c 1/(c-3)-1/c=3/(c(c-3))