Understanding Least Common Multiple (LCM)

This video tutorial explains how to determine the least common multiple (LCM) of two numbers using two methods: listing multiples and prime factorization. The LCM is the smallest positive integer that is a multiple of both numbers. The video provides examples, including finding the LCM of 4 and 6, 6 and 8, and 60 and 72, demonstrating both methods. The prime factorization method involves using the highest power of each prime factor present in the numbers. The tutorial emphasizes that listing multiples is practical for small numbers, while prime factorization is more efficient for larger numbers.

What is the least common multiple of two integers?

• The difference between the two integers.

• The smallest positive integer that is a multiple of both integers.

• The sum of the two integers.

• The largest number that divides both integers without a remainder.

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

• Listing the multiples of each number and finding the smallest common one.

• Adding the numbers until they match.

• Subtracting the numbers repeatedly.

• Dividing the numbers by their greatest common divisor.

What is the LCM of 4 and 6 using the listing method?

• 8

• 12

• 14

• 10

When listing multiples, what is the LCM of 6 and 8?

• 24

• 20

• 18

• 16

What is the alternative method to find the LCM for larger numbers?

• Using the average of the numbers.

• Using prime factorization.

• Using the difference of the numbers.

• Using the sum of the numbers.

In prime factorization, what do you do with the prime factors to find the LCM?

• Add them together.

• Multiply them by the smallest power.

• Subtract them from each other.

• Raise them to the highest power found in either number.

What is the LCM of 36 and 54 using prime factorization?

• 180

• 144

• 108

• 72

What is the prime factorization of 60?

• 2^2 * 3 * 5

• 2^3 * 3 * 5

• 2 * 3^2 * 5

• 2 * 3 * 5^2

What is the LCM of 60 and 72 using prime factorization?

• 360

• 300

• 420

• 240

Which of the following is true about the LCM of two numbers?

• It is the sum of the two numbers.

• It is the smallest number divisible by both numbers.

• It is always smaller than both numbers.

• It is the largest number that can divide both numbers.