Least Common Multiple and Prime Factorization

The video tutorial covers divisibility problems often found in standardized exams. It explains how to determine if a number is divisible by both 12 and 20 using prime factorization. The least common multiple (LCM) is used to find the smallest number divisible by both. The tutorial also provides an example with numbers 9 and 24, demonstrating how to apply these concepts to solve problems. The focus is on understanding prime factors and using them to determine divisibility.

What is the key concept to understand when determining if a number is divisible by both 12 and 20?

• It must be divisible by 10.

• It must be a multiple of 100.

• It must be divisible by the prime factors of both 12 and 20.

• It must be an even number.

What is the prime factorization of 12?

• 2 x 5 x 5

• 2 x 2 x 3

• 2 x 3 x 5

• 3 x 3 x 2

Which of the following is the least common multiple of 12 and 20?

• 40

• 100

• 80

• 60

If a number is divisible by both 12 and 20, which of the following must it also be divisible by?

• 7

• 8

• 9

• 12

What is the prime factorization of 20?

• 2 x 5 x 5

• 5 x 5

• 2 x 3 x 3

• 2 x 2 x 5

What is the least common multiple of 9 and 24?

• 72

• 96

• 36

• 48

Which of the following numbers is divisible by both 9 and 24?

• 11

• 16

• 72

• 27

Which combination of prime factors would be divisible by both 9 and 24?

• 2 x 2 x 2

• 3 x 3 x 3

• 5 x 5

• 2 x 3 x 3

If a number is divisible by 9 and 24, which of the following must it also be divisible by?

• 27

• 11

• 8

• 5

Which of the following is not a factor of the least common multiple of 9 and 24?

• 5

• 18

• 4

• 6