# How can the prime factorization of a number be used to find the LCM and GCF of two or more numbers?

## How can the prime factorization of a number be used to find the LCM and GCF of two or more numbers?

1 Answer. First find all the prime factors. For GCF find all the factors that are same and multiply. For LCM find all the factors that are different, and multiply.

Can you use prime factorization to find LCM?

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

### What is the LCM of 18 and 24 using prime factorization?

72
LCM of 18 and 24 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 23 × 32 = 72. Hence, the LCM of 18 and 24 by prime factorization is 72.

What are the different methods in finding the GCF and LCM?

To find the GCF, multiply all the common factors (the numbers to the left outside the slide-forms the number “1”) To find the LCM, multiple all the common factors and the numbers on the bottom (all the numbers on the left outside the slide, and underneath the slide-forms a big “L”)

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

Prime factorization of 12 and 36 is (2 × 2 × 3) = 22 × 31 and (2 × 2 × 3 × 3) = 22 × 32 respectively. LCM of 12 and 36 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 22 × 32 = 36. Hence, the LCM of 12 and 36 by prime factorization is 36.

What is the LCM of 12 and 20 using prime factorization?

60
LCM of 12 and 20 by Prime Factorization LCM of 12 and 20 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 22 × 31 × 51 = 60. Hence, the LCM of 12 and 20 by prime factorization is 60.

## How do you find GCF?

The greatest common factor is the greatest factor that divides both numbers. To find the greatest common factor, first list the prime factors of each number. 18 and 24 share one 2 and one 3 in common. We multiply them to get the GCF, so 2 * 3 = 6 is the GCF of 18 and 24.

What is the GCF of 12 and 20 using prime factorization?

2 × 2 = 4
GCF of 12 and 20 by Prime Factorization Hence, the GCF of 12 and 20 is 2 × 2 = 4.

### What is the LCM of 32 and 48?

96
The LCM of 32 and 48 is 96.

What is the purpose of using prime factorization?

Calculates the GCF using the prime factorization algorithms,

• Finds the prime factorizations of the given numbers,
• Indicates the common prime factors and
• Graphically illustrates the factorization trees of the given numbers.
• #### What are some real life applications of GCF and LCM?

How can you tell if a word problem requires you to use

• Greatest Common Factor
• or Least Common Multiple
• to solve?
• How do you find the LCM using GCF?

Find all the prime factors of each given number and write them in exponent form.

• List all the prime numbers found,using the highest exponent found for each.
• Multiply the list of prime factors with exponents together to find the LCM.