# Algebra Examples

, ,

Step 1

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 2

Step 2.1

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 2.2

Since has no factors besides and .

is a prime number

Step 2.3

Since has no factors besides and .

is a prime number

Step 2.4

has factors of and .

Step 2.5

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

Step 2.6

Multiply .

Step 2.6.1

Multiply by .

Step 2.6.2

Multiply by .

Step 3

Find the GCF of the denominators .

Step 4

Divide by .