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 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 each term.

Cancel the common factor of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Apply the distributive property.

Move to the left of .

Rewrite using the commutative property of multiplication.

Multiply by by adding the exponents.

Move .

Multiply by .

Cancel the common factor of .

Move the leading negative in into the numerator.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Factor out of .

Rewrite as .

Factor out of .

Reorder terms.

Raise to the power of .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Multiply by .

Simplify .

Cancel the common factor of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Apply the distributive property.

Simplify the expression.

Multiply by .

Move to the left of .

Apply the distributive property.

Multiply by .

Set the equation equal to zero.

Move all the expressions to the left side of the equation.

Move to the left side of the equation by subtracting it from both sides.

Move to the left side of the equation by adding it to both sides.

Simplify .

Add and .

Subtract from .

Factor the left side of the equation.

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Rewrite as .

Expand using the FOIL Method.

Apply the distributive property.

Apply the distributive property.

Apply the distributive property.

Simplify and combine like terms.

Simplify each term.

Multiply by .

Multiply by .

Multiply by .

Multiply by .

Multiply by .

Multiply by .

Subtract from .

Add and .

Add and .

Add and .

Factor.

Rewrite in a factored form.

Rewrite as .

Reorder and .

Since both terms are perfect squares, factor using the difference of squares formula, where and .

Remove unnecessary parentheses.

Replace the left side with the factored expression.

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Divide by .

If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .

Set the first factor equal to and solve.

Set the first factor equal to .

Subtract from both sides of the equation.

Set the next factor equal to and solve.

Set the next factor equal to .

Subtract from both sides of the equation.

Multiply each term in by

Multiply each term in by .

Multiply .

Multiply by .

Multiply by .

Multiply by .

The final solution is all the values that make true.

Exclude the solutions that do not make true.

Solve for n 1/(n-4)-2/n=3/(4-n)