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.

The number is not a prime number because it only has one positive factor, which is itself.

Not prime

has factors of and .

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 by .

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 .

Simplify each term.

Rewrite using the commutative property of multiplication.

Combine and .

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Apply the distributive property.

Multiply by .

Multiply by .

Cancel the common factor of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Add and .

Simplify .

Rewrite using the commutative property of multiplication.

Multiply .

Combine and .

Multiply by .

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 .

Multiply each term in by

Multiply each term in by .

Multiply .

Multiply by .

Multiply by .

Multiply by .

Solve for x (5-x)/x+3/4=7/x