Finding GCF and LCM through Prime Factorization

This video tutorial explains how to find the greatest common factor (GCF) and least common multiple (LCM) of three or more numbers using prime factorization. It provides two examples, demonstrating the process of breaking down numbers into their prime factors to identify common factors for GCF and the highest power of each prime for LCM. The tutorial emphasizes the differences in approach when dealing with more than two numbers and highlights the efficiency of using prime factorization for these calculations.

What is the first step in finding the greatest common factor (GCF) of three numbers?

• Divide the largest number by the smallest number.

• Add the numbers together.

• Perform the prime factorization of each number.

• List all the multiples of each number.

Which of the following is a prime factor of 12?

• 8

• 6

• 4

• 3

What is the greatest common factor (GCF) of 12, 15, and 21?

• 7

• 1

• 3

• 5

When finding the least common multiple (LCM) of three numbers, what should you do after identifying the prime factors?

• Multiply the prime factors together.

• Find the highest power of each prime factor.

• Find the lowest power of each prime factor.

• Add the prime factors together.

What is the least common multiple (LCM) of 12, 15, and 21?

• 120

• 60

• 420

• 180

Which of the following is a prime factor of 24?

• 6

• 4

• 8

• 2

What is the greatest common factor (GCF) of 24, 32, and 50?

• 10

• 2

• 8

• 4

How many times does the prime factor 2 appear in the prime factorization of 32?

• 2

• 3

• 4

• 5

What is the least common multiple (LCM) of 24, 32, and 50?

• 2400

• 1200

• 3600

• 4800

Why is prime factorization useful for finding the LCM of multiple numbers?

• It helps in listing all multiples.

• It simplifies the addition of numbers.

• It helps in identifying the highest power of each prime factor.

• It makes division easier.