# Algebra Examples

, ,

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

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

1. Find the LCM of and .

2. Find the LCM of and .

3. .

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 prime factorization of is .

has factors of and .

has factors of and .

: Occurs times.

has factors of and .

: Occurs times.

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 LCM of is .

Multiply by by adding the exponents.

Combine and

Raise to the power of .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Multiply by by adding the exponents.

Combine and

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Raise to the power of .

Find the GCF of the denominators .

Divide by .