Understanding Least Common Multiple (LCM)

In this video, Mr. J explains how to find the least common multiple (LCM) of three numbers using two methods: listing multiples and prime factorization. The video begins with an introduction to the concept of multiples and the LCM. It then demonstrates the listing multiples method with numbers 5, 8, and 20, showing how to extend the list to find the LCM. The second method, prime factorization, is explained using numbers 21, 28, and 32, detailing how to break down numbers into prime factors and match them to find the LCM. The video concludes with a summary of both methods.

What is the Least Common Multiple (LCM) of two or more numbers?

• The largest number that is a multiple of all the numbers.

• The smallest number that is a multiple of all the numbers.

• The largest number that is a factor of all the numbers.

• The smallest number that is a factor of all the numbers.

Which of the following is a method to find the LCM?

• Adding the numbers together.

• Dividing the numbers by their greatest common factor.

• Listing out the multiples of the numbers.

• Subtracting the smaller number from the larger number.

When listing multiples to find the LCM, what should you do if no common multiple is found initially?

• Multiply all the numbers together.

• Choose the smallest number as the LCM.

• Stop and choose the largest number as the LCM.

• List more multiples until a common one is found.

What is the LCM of 5, 8, and 20 using the listing multiples method?

• 80

• 20

• 40

• 60

Why might prime factorization be preferred over listing multiples for finding the LCM?

• It is more accurate for all numbers.

• It is faster for smaller numbers.

• It is easier for larger numbers.

• It requires less mathematical knowledge.

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

• Add all the numbers together.

• List the prime factors of each number.

• Divide the numbers by their greatest common factor.

• Multiply all the numbers together.

In prime factorization, how do you determine which prime factors to use for the LCM?

• Use the highest power of each prime factor present.

• Use only the smallest prime factors.

• Use the lowest power of each prime factor present.

• Use only the prime factors of the largest number.

What is the LCM of 21, 28, and 32 using prime factorization?

• 672

• 336

• 168

• 84

Which of the following is NOT a step in the prime factorization method?

• Add the prime factors together.

• Match the prime factors vertically.

• List the prime factors of each number.

• Multiply the highest power of each prime factor.

What is the benefit of matching prime factors vertically in the prime factorization method?

• It reduces the number of calculations needed.

• It simplifies the addition of factors.

• It ensures all prime factors are considered.

• It helps in finding the greatest common factor.