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Trigonometry Examples
Step 1
Step 1.1
Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
Step 1.2
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.
Step 1.3
The number is not a prime number because it only has one positive factor, which is itself.
Not prime
Step 1.4
Since has no factors besides and .
is a prime number
Step 1.5
The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either number.
Step 1.6
The factor for is itself.
occurs time.
Step 1.7
The LCM of is the result of multiplying all factors the greatest number of times they occur in either term.
Step 1.8
The Least Common Multiple of some numbers is the smallest number that the numbers are factors of.
Step 2
Step 2.1
Multiply each term in by .
Step 2.2
Simplify the left side.
Step 2.2.1
Rewrite using the commutative property of multiplication.
Step 2.2.2
Multiply .
Step 2.2.2.1
Combine and .
Step 2.2.2.2
Multiply by .
Step 2.2.3
Cancel the common factor of .
Step 2.2.3.1
Cancel the common factor.
Step 2.2.3.2
Rewrite the expression.
Step 2.3
Simplify the right side.
Step 2.3.1
Cancel the common factor of .
Step 2.3.1.1
Cancel the common factor.
Step 2.3.1.2
Rewrite the expression.
Step 2.3.2
Apply the distributive property.
Step 2.3.3
Multiply by .
Step 3
Step 3.1
Rewrite the equation as .
Step 3.2
Move all terms not containing to the right side of the equation.
Step 3.2.1
Add to both sides of the equation.
Step 3.2.2
Add and .
Step 3.3
Divide each term in by and simplify.
Step 3.3.1
Divide each term in by .
Step 3.3.2
Simplify the left side.
Step 3.3.2.1
Cancel the common factor of .
Step 3.3.2.1.1
Cancel the common factor.
Step 3.3.2.1.2
Divide by .
Step 4
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Mixed Number Form: