 # To find Least Common Multiple by using Prime Factorization Method – Definition, Facts, Examples

Prime numbers have only two factors. The prime factorization of a number is the product of the prime numbers that equals the number. One way to find the prime factorization of a number is to make a factor tree. Know how to find Least Common Multiple by using Prime Factorization Method from here.

Multiply the product with other grouped factors to find the L.C.M by using the prime factorization method. For your convenience, we have provided some examples on how to find the Least Common Multiple by using the Prime Factorization Method with step by step explanation at the end of this page.

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## How to find LCM by Prime Factorization Method?

One of the reasons we look at the multiples and primes is to use these techniques to find the LCM of two numbers. This is used to add or subtract the fractions.
1. Find the prime factorization of each number.
2. Write each number as a product of primes, matching primes vertically when possible.
3. Bring down the primes in each column.
4. Multiply the factors to get the least common multiple.

### Finding the LCM by Prime Factorization Method Examples

Example 1.
What is the least common multiple of 50 and 100 by using the prime factorization method?
Solution:
List all prime factors for each number.
Prime Factorization of 50 is 2 × 5 × 5
Prime Factorization of 100 is 2 × 2 × 5 × 5
For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.
The new superset list is
2, 2, 5, 5
Multiply these factors together to find the LCM.
LCM = 2 x 2 x 5 x 5 = 100
Thus, LCM(50, 100) = 100

Example 2.
What is the least common multiple of 12 and 20 by using the prime factorization method?
Solution:
List all prime factors for each number.
Prime Factorization of 12 is 2 × 2 × 3
Prime Factorization of 20 is 2 × 2 × 5
For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.
The new superset list is
2, 2, 3, 5
Multiply these factors together to find the LCM.
The least common multiples of 12 and 20 = 2 x 2 x 3 x 5 = 60
Thus, LCM(12, 20) = 60

Example 3.
What is the least common multiple of 6 and 15 by using the prime factorization method?
Solution:
List all prime factors for each number.
Prime Factorization of 6 is 2 × 3
Prime Factorization of 15 is 3 × 5
For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.
The new superset list is
2, 3, 5
Multiply these factors together to find the LCM.
The least common multiples of 6 and 15 = 2 x 3 x 5 = 30
Thus, LCM(6, 15) = 30

Example 4.
What is the least common multiple of 25, 30 and 45 by using the prime factorization method?
Solution:
List all prime factors for each number.
Prime Factorization of 25 is 5 × 5
Prime Factorization of 30 is 2 × 3 × 5
Prime Factorization of 45 is 3 × 3 × 5
For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.
The new superset list is
2, 3, 3, 5, 5
Multiply these factors together to find the LCM.
The least common multiples of 25, 30 and 45 = 2 x 3 x 3 × 5 × 5 = 450
Thus, LCM(25, 30, 45) = 450

Example 5.
What is the least common multiple of 12, 15 and 75 by using the prime factorization method?
Solution:
List all prime factors for each number.
Prime Factorization of 12 is 2 × 2 × 3
Prime Factorization of 15 is 3 × 5
Prime Factorization of 75 is 3 × 5 × 5
For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.
The new superset list is
2, 2, 3, 5, 5
Multiply these factors together to find the LCM.
LCM = 2 x 2 x 3 × 5 × 5 = 300
Thus, the LCM(12, 15, 75) is 300.

Make use of 5th Grade Math Problems to get more related topics such as practice tests, worksheets, word problems, etc easily and quickly and score good marks in the exams.

### FAQ’s to find Least Common Multiple Using Prime Factorization

1. How do you find the least common multiple using prime factorization?

Write each number as a product of primes, match the prime factors vertically when possible. Bring down the primes in each column. Multiply the factors to get the LCM.

2. What are the three methods in finding the LCM?

The different methods to find the LCM is
1. Listing Multiples
2. Prime factorization method
3. Division method

3. What is the LCM of 12 and 36 using prime factorization?

The Least Common Multiple of 12 and 36 is 36.

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