# Algebra Examples

, ,
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. .
Calculate the LCM of the numerators to get .
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.
Since has no factors besides and .
is a prime number
The prime factorization of is .
has factors of and .
has factors of and .
: Occurs times.
: Occurs time.
has factors of and .
: Occurs time.
: Occurs time.
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 to get .
Multiply by to get .
Multiply by to get .
Multiply by to get .
Find the GCF of the denominators to get .
Divide by to get .