Exploring Least Common Multiple with Prime Factorization

The video tutorial explains how to find the least common multiple (LCM) of 30 and 25 using the prime factorization method. It begins by breaking down the numbers into their prime factors: 30 as 2, 3, and 5, and 25 as 5 and 5. The LCM is then constructed by taking the highest power of each prime number present in the factorizations, resulting in 2, 3, and two 5s. The product of these numbers gives the LCM, which is 150. The tutorial concludes by verifying the result and emphasizing the importance of including all necessary prime factors.

What is the first step in finding the least common multiple (LCM) of 30 and 25?

• Subtract the smaller number from the larger number

• Find the prime factorization of each number

• Divide the larger number by the smaller number

• Add the two numbers

Which of the following is the prime factorization of 30?

• 2 x 2 x 3

• 5 x 5

• 2 x 3 x 5

• 3 x 5 x 5

What is the prime factorization of 25?

• 2 x 3 x 5

• 2 x 2 x 5

• 5 x 5

• 3 x 5 x 5

To find the LCM, why do we need to include all prime factors from both numbers?

• To ensure the LCM is the smallest number divisible by both

• To make the calculation easier

• To find the greatest common divisor

• To simplify the numbers

Which prime factors must be included to ensure the LCM is divisible by 30?

• 3 x 3 x 5

• 5 x 5

• 2 x 3 x 5

• 2 x 2 x 3

Why do we need to add an extra 5 to the prime factorization when finding the LCM of 30 and 25?

• To ensure it is divisible by 30

• To simplify the calculation

• To ensure it is divisible by 25

• To make the number larger

What happens if we remove the factor of 2 from the LCM?

• It will no longer be divisible by 30

• It will still be divisible by 30

• It will no longer be divisible by 25

• It will still be divisible by 25

What is the least common multiple (LCM) of 30 and 25?

• 150

• 200

• 100

• 75

How can we verify that our calculated LCM is correct?

• By checking if it is divisible by both 30 and 25

• By adding the two numbers

• By subtracting the smaller number from the larger number

• By dividing the larger number by the smaller number

What is the final step in finding the LCM of 30 and 25?

• Multiplying the prime factors together

• Adding the two numbers

• Dividing the larger number by the smaller number

• Subtracting the smaller number from the larger number