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

The factors for are , which is multiplied by each other times.

occurs times.

The factor for is itself.

occurs time.

The factors for are , which is multiplied by each other times.

occurs times.

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

Multiply by .

The LCM for is the numeric part multiplied by the variable part.

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

Simplify each term.

Rewrite using the commutative property of multiplication.

Combine and .

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Rewrite using the commutative property of multiplication.

Combine and .

Cancel the common factor of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Simplify .

Rewrite using the commutative property of multiplication.

Cancel the common factor of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Move all terms not containing to the right side of the equation.

Subtract from both sides of the equation.

Subtract from .

Divide each term by and simplify.

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

Mixed Number Form: