Least Common Multiple Concepts

The video tutorial explains how to find the least common multiple (LCM) of two numbers. It begins with an introduction to the concept of LCM, followed by a detailed explanation of prime factorization. The tutorial then outlines the steps to find the LCM by identifying the greatest number of times each prime factor appears in any factorization. The calculation of the LCM is demonstrated using the example of numbers 4 and 15, resulting in an LCM of 60. The video concludes with a clarification of what LCM means, emphasizing that it is the smallest number that is a multiple of both given numbers.

What is the first step in finding the least common multiple of two numbers?

• Add the two numbers together.

• Find the prime factorization of each number.

• Multiply the two numbers.

• Subtract the smaller number from the larger number.

What is the prime factorization of 15?

• 2 x 7

• 2 x 3

• 3 x 5

• 5 x 5

Which of the following is a prime factor of 4?

• 3

• 5

• 2

• 7

How do you determine the least common multiple from the prime factorizations?

• Multiply the greatest occurrence of each prime factor.

• Add all the prime factors together.

• Divide the largest prime factor by the smallest.

• Multiply the smallest occurrence of each prime factor.

Which prime factor occurs most frequently in the factorization of 4?

• 7

• 5

• 3

• 2

What is the least common multiple of 4 and 15?

• 45

• 30

• 75

• 60

What is the least common multiple of 2 and 3?

• 9

• 5

• 12

• 6

What is the least common multiple of 5 and 10?

• 25

• 10

• 20

• 15

Which prime factor is included only once in the LCM of 4 and 15?

• 7

• 2

• 3

• 5

What is the least common multiple of 6 and 8?

• 30

• 12

• 18

• 24