# Algebra Examples

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 two steps to find the LCM. Find LCM for the numeric part then find LCM for the variable part .

The LCM is the smallest 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

Since has no factors besides and .

is a prime 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.

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

Simplify each term.

Move to the left of the expression .

Multiply by .

Multiply by .

Cancel the common factor of .

Move the leading negative in into the numerator.

Write as a fraction with denominator .

Factor out the greatest common factor .

Cancel the common factor.

Rewrite the expression.

Simplify.

Multiply and .

Divide by .

Multiply by .

Use the quadratic formula to find the solutions.

Substitute the values , , and into the quadratic formula and solve for .

Simplify.

Simplify the numerator.

Raise to the power of .

Multiply by .

Multiply by .

Add and .

Rewrite as .

Factor out of .

Rewrite as .

Pull terms out from under the radical.

Multiply by .

Simplify .

Factor out of .

Multiply by .

Multiply by .

The final answer is the combination of both solutions.

The result can be shown in multiple forms.

Exact Form:

Decimal Form: