# Algebra Examples

, ,

Step 1

Step 1.1

Factor out of .

Step 1.2

Cancel the common factors.

Step 1.2.1

Factor out of .

Step 1.2.2

Cancel the common factor.

Step 1.2.3

Rewrite the expression.

Step 2

To find the LCM for a list of fractions such as using GCF:

1. Find the LCM of and .

2. Find the GCF of and .

3. .

Step 3

Step 3.1

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 3.2

The prime factors for are .

Step 3.2.1

has factors of and .

Step 3.2.2

has factors of and .

Step 3.3

has factors of and .

Step 3.4

Since has no factors besides and .

is a prime number

Step 3.5

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

Step 3.6

Multiply .

Step 3.6.1

Multiply by .

Step 3.6.2

Multiply by .

Step 4

Find the GCF of the denominators .

Step 5

Divide by .