Understanding GCF and LCM

The video tutorial explains how to determine the greatest common factor (GCF) and the least common multiple (LCM) of the numbers 72 and 96. It uses prime factorization and Venn diagrams to illustrate the process. The prime factorization of 72 is shown as 2^3 * 3^2, and for 96 as 2^5 * 3. The Venn diagram helps identify common factors for the GCF, which is 24, and all factors for the LCM, which is 288. The tutorial provides a step-by-step guide to understanding these concepts.

What are the two mathematical concepts being explored in this tutorial?

• Addition and Subtraction

• Greatest Common Factor and Least Common Multiple

• Multiplication and Division

• Square Roots and Exponents

What is the prime factorization of 72?

• 2^3 * 3^2

• 2^2 * 3^3

• 2^4 * 3

• 2^3 * 3

How many factors of 2 are there in the prime factorization of 96?

• Six

• Five

• Four

• Three

What is the purpose of using a Venn diagram in this context?

• To visualize the addition of numbers

• To find the intersection of prime factors

• To calculate the sum of numbers

• To compare the sizes of numbers

Which prime factors are common between 72 and 96?

• Five factors of 2 and one factor of 3

• Four factors of 2 and two factors of 3

• Three factors of 2 and one factor of 3

• Two factors of 2 and one factor of 3

What is the greatest common factor (GCF) of 72 and 96?

• 18

• 12

• 24

• 36

What additional factor is needed in the Venn diagram to complete the prime factors of 72?

• Two more factors of 2

• Two more factors of 3

• One more factor of 3

• One more factor of 2

How many total factors of 2 are needed to represent 96 in the Venn diagram?

• Three

• Four

• Five

• Six

What is the least common multiple (LCM) of 72 and 96?

• 144

• 192

• 288

• 240

Why is 288 considered the least common multiple of 72 and 96?

• It is the largest number that divides both

• It is the smallest number that is a multiple of both

• It is the average of both numbers

• It is the sum of both numbers