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 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.

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

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 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 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.

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Apply the distributive property.

Multiply by .

Rewrite using the commutative property of multiplication.

Multiply .

Combine and .

Multiply by .

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Cancel the common factor of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Move all terms containing to the left side of the equation.

Subtract from both sides of the equation.

Subtract from .

Factor using the AC method.

Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .

Write the factored form using these integers.

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 .

Add to both sides of the equation.

Set the next factor equal to and solve.

Set the next factor equal to .

Add to both sides of the equation.

The final solution is all the values that make true.

Solve for r (r-13)/5+9/r=1/5