Finding the Least Common Denominator Techniques

The video tutorial by Mr. Witte from Fort Bend Tutoring covers the process of finding the Least Common Denominator (LCD) and the Lowest Common Multiple (LCM). It explains two main methods: using multiples and prime factorization. The tutorial provides step-by-step examples, including algebraic expressions, to demonstrate these methods. It also offers shortcuts and tips for efficiency. The video concludes with a call to action for viewers to subscribe and engage with additional resources.

What is the relationship between the Least Common Denominator (LCD) and the Lowest Common Multiple (LCM)?

• LCD is used for fractions, while LCM is used for whole numbers.

• They are completely different concepts.

• They are the same process but used in different contexts.

• LCD is always larger than LCM.

When finding the LCD/LCM by listing multiples, what is the first common multiple of 9 and 15?

• 27

• 18

• 45

• 36

Which of the following is a step in finding the LCD/LCM using prime factorization?

• Dividing the numbers by their greatest common divisor.

• Adding the prime factors together.

• Finding the highest power of each prime factor.

• Listing all multiples of the numbers.

What is the prime factorization of 15?

• 3 x 5

• 3 x 3

• 5 x 5

• 2 x 7

In the example of finding the LCD/LCM for 20 and 40, what is the shortcut mentioned?

• Multiply the two numbers together.

• Use the larger number if the smaller number divides it evenly.

• Always use the smaller number.

• Subtract the smaller number from the larger number.

What is the prime factorization of 40?

• 2 x 2 x 2 x 5

• 2 x 3 x 5

• 2 x 2 x 5

• 2 x 5 x 5

When comparing 4x^2y^5 and 10x^3y, what is the highest power of x needed for the LCD/LCM?

• x^5

• x^2

• x^3

• x^4

For the algebraic expressions X+3 and X-1, how do you find the LCD/LCM?

• Add the expressions together.

• Subtract the smaller expression from the larger one.

• Multiply the expressions together.

• Divide the larger expression by the smaller one.

What is the factorization of the quadratic trinomial x^2 + 6x + 9?

• (x + 3)(x + 3)

• (x + 2)(x + 4)

• (x + 1)(x + 5)

• (x + 3)(x + 2)

In the final example, what is the simplified form of the LCD/LCM for the expressions x^2 + 6x + 9 and x^2 + 8x + 15?

• (x + 3)^2(x + 5)^2

• (x + 3)^2(x + 5)

• (x + 3)(x + 5)^2

• (x + 3)(x + 5)