Finding the Least Common Multiple

The video tutorial explains how to find the least common multiple (LCM) of numbers including a variable. It starts with the problem statement and proceeds to find the prime factorization of the given numbers. The tutorial then calculates the LCM without considering the variable K and finally determines the smallest possible value of K that satisfies the LCM condition.

What is the main focus of the video tutorial?

• Finding the greatest common divisor

• Solving quadratic equations

• Finding the least common multiple involving a variable

• Understanding prime numbers

Which numbers are involved in the LCM problem presented in the video?

• 5, 10, 15, and K

• 10, 15, 25, and K

• 8, 16, 24, and K

• 12, 15, 20, and K

What is the given LCM of the numbers 12, 15, 20, and K?

• 240

• 420

• 480

• 360

What is the prime factorization of the number 12?

• 3 x 3 x 2

• 2 x 2 x 3

• 2 x 3 x 5

• 2 x 2 x 5

What is the prime factorization of the number 15?

• 2 x 5

• 5 x 5

• 3 x 5

• 2 x 3

What is the prime factorization of the number 20?

• 2 x 2 x 5

• 3 x 3 x 5

• 2 x 2 x 3

• 2 x 3 x 5

How is the LCM determined from the prime factors?

• By multiplying the highest power of each prime factor

• By adding all the prime factors

• By subtracting the smallest prime factor

• By dividing the largest prime factor

What does the term 'least' refer to in the context of LCM?

• The smallest number

• The greatest number

• The smallest common factor

• The greatest common factor

What is the LCM of 12, 15, and 20 without considering K?

• 60

• 240

• 120

• 180

What factor is needed to multiply with 60 to get the LCM of 420?

• 6

• 5

• 8

• 7