LCM: Prime Factorization Method

It is recommended to practice using the Prime Factorization Method to become proficient in finding the LCM of numbers.

The Least Common Multiple of two numbers is the smallest number that is a multiple of both numbers.

The Prime Factorization Method involves creating a set of prime factors from two numbers in a way that avoids unnecessary duplicates, allowing you to find the least common multiple.

Prime factorization is found by breaking down a number into the prime factors that multiply together to get that number.

The prime factorization of 12 is 2 x 2 x 3.

The prime factorization of 14 is 2 x 7.

To build the prime factorization of the LCM, combine the prime factors from two numbers, including non-overlapping factors and only one copy of overlapping factors.

The prime factorization of the LCM of 12 and 14 is 2 x 2 x 3 x 7.

The LCM of 12 and 14 is 84.

Leaving out duplicates ensures you are getting the smallest number that is divisible by each of the original numbers, achieving the least common multiple.

If there are no overlapping factors, the LCM will be the product of the original numbers.

An example is the numbers 9 and 10, which results in an LCM of 90.

The prime factorization of 105 is 3 x 5 x 7.

The prime factorization of 120 is 2 x 2 x 2 x 3 x 5.

Identify overlapping prime factors (3 and 5) and use only one copy. Include non-overlapping prime factors from both numbers to form the set for LCM.

The LCM of 105 and 120 is 840.

The Prime Factorization Method is useful because it saves work compared to listing multiples for each number to find the LCM.

It is recommended to practice using the Prime Factorization Method to become proficient in finding the LCM of numbers.

The Least Common Multiple of two numbers is the smallest number that is a multiple of both numbers.