Finding the Least Common Multiple with Variables

This video tutorial teaches how to find the least common multiple (LCM) involving variables. It begins with a simple example using numbers, explaining the process of finding factors and using prime factorization. The tutorial then applies this method to variables and polynomials, demonstrating how to find the LCM by taking the highest power of each factor. The video concludes with examples of using LCM to find common denominators in fractions.

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

• Find the prime factors of each number

• Subtract the smaller number from the larger number

• Divide the numbers by their greatest common divisor

• Add the numbers together

Which of the following is the prime factorization of 20?

• 2 x 2 x 2 x 5

• 4 x 5

• 2 x 10

• 2^2 x 5

When finding the LCM, which factor should you take?

• The smallest factor

• The factor that occurs the least

• The largest factor

• The factor that occurs the most

What is the LCM of 14 and 20?

• 70

• 280

• 140

• 28

In the example with variables, what is the LCM of 8 and 20?

• 160

• 80

• 320

• 40

How do you factor x^2 - 9?

• (x - 1)(x + 9)

• (x - 9)(x + 1)

• (x - 3)(x - 3)

• (x - 3)(x + 3)

What two numbers multiply to -12 and add to -1?

• -2 and 6

• -4 and 3

• -3 and 4

• -6 and 2

Which of the following is a binomial?

• x^2 - 9

• x + 1

• x^2 + 3x - 4

• x^3 - 3x^2 + 2x - 1

What is the LCM of x^2 - 9 and x^2 + 3x - 4?

• (x + 3)(x - 3)(x + 4)

• (x - 3)(x - 3)(x + 4)

• (x + 3)(x - 3)(x - 4)

• (x + 3)(x + 3)(x - 4)

What is the purpose of finding the least common multiple in the context of rational expressions?

• To subtract the expressions

• To simplify the expressions

• To add the expressions

• To find a common denominator