Understanding GCF and LCM through Prime Factorization

In this video, Mr. J explains how to find the greatest common factor (GCF) and least common multiple (LCM) of three numbers using prime factorization. He demonstrates the process with examples, starting with the GCF of 54, 36, and 90, and then the LCM of 21, 28, and 32. The video emphasizes the efficiency of prime factorization for larger numbers, providing a clear, step-by-step approach to solving these mathematical problems.

Why is prime factorization preferred for finding GCF and LCM of larger numbers?

• It is easier for smaller numbers.

• It is the only method available.

• It doesn't require any calculations.

• It is faster than listing all factors or multiples.

What is the first step in finding the GCF of 54, 36, and 90 using prime factorization?

• Divide the numbers by 2.

• List all multiples of the numbers.

• Find the prime factorization of each number.

• Add the numbers together.

Which of the following is a common prime factor of 54, 36, and 90?

• 7

• 5

• 11

• 2

How do you calculate the GCF once you have the common prime factors?

• Divide the common prime factors.

• Subtract the common prime factors.

• Multiply the common prime factors.

• Add the common prime factors.

What is the first step in finding the LCM of 21, 28, and 32 using prime factorization?

• List all factors of the numbers.

• Subtract the smallest number from the largest.

• Find the prime factorization of each number.

• Multiply the numbers together.

When matching prime factors vertically for LCM, what should you do if a number appears in multiple columns?

• Ignore the number.

• Bring down only one occurrence of the number.

• Add the numbers together.

• Bring down all occurrences of the number.

What is the result of multiplying the numbers brought down from each column when calculating the LCM?

• The sum of the numbers.

• The difference between the numbers.

• The least common multiple.

• The greatest common factor.

Which of the following is NOT a step in finding the LCM using prime factorization?

• Bringing down numbers to represent columns.

• Listing prime factors vertically.

• Multiplying the numbers brought down.

• Adding all the numbers together.

What is the LCM of 21, 28, and 32 as calculated in the video?

• 128

• 56

• 672

• 84

What is the purpose of using prime factorization for GCF and LCM?

• To make the process more complex.

• To simplify the process for larger numbers.

• To avoid using multiplication.

• To only work with even numbers.