Understanding Least Common Multiple (LCM)

This video tutorial explains how to determine the least common multiple (LCM) of two terms. It begins with an introduction to the concept of LCM, followed by a method of finding LCM by listing multiples. The tutorial then introduces a more efficient method using prime factorization, demonstrating with examples, including terms with variables. The video concludes with a complex example, reinforcing the prime factorization method for finding LCM.

What is the least common multiple (LCM) of two numbers?

• The difference between the two numbers

• The sum of the two numbers

• The smallest positive number that is a multiple of both numbers

• The largest number that divides both numbers

When listing multiples to find the LCM of 4 and 6, which number is the LCM?

• 6

• 12

• 24

• 8

Why is listing multiples not practical for large numbers?

• It only works for even numbers

• It requires a calculator

• It is too time-consuming

• It is not accurate

What is the first step in finding the LCM using prime factorization?

• List all multiples

• Divide the numbers

• Add the numbers

• Find the prime factors of each number

In the prime factorization method, how do you determine the number of times a factor should be included in the LCM?

• By multiplying the occurrences in both numbers

• By taking the maximum number of occurrences in either number

• By taking the minimum number of occurrences in either number

• By adding the occurrences in both numbers

What is the LCM of 24 and 30 using prime factorization?

• 120

• 150

• 90

• 60

When variables are included, what remains unchanged in the LCM finding process?

• The need to list all multiples

• The use of prime factorization

• The addition of all factors

• The subtraction of factors

In the example with variables, what is the LCM of 27x²y² and 15x³y?

• 135x³y

• 135x²y²

• 135x³y²

• 135x²y

What is the LCM of 60 and 72 with variables m and n?

• 360m⁵n³

• 360m⁴n⁴

• 360m⁴n⁵

• 360m⁵n⁴

What is the final step in finding the LCM using prime factorization?

• Subtract the factors

• Multiply the selected factors

• Divide the factors

• Add the factors