It looks like you've uploaded an image related to a set of questions on determining the least common multiple (LCM) of expressions. I will review the content and provide solutions to each of the questions.

Let's start with analyzing the questions:

1. Question 5: Determine the LCM of $8v^2 - 6v$ and $3$.
2. Question 6: Determine the LCM of $(b+6)(b+2)$ and $4(b+2)$.
3. Question 7: Determine the LCM of $(x+3)$ and $(x-3)$.

Let me provide detailed solutions for each.

Solution to Question 5:

The expression $8v^2 - 6v$ can be factored as: $8v^2 - 6v = 2v(4v - 3)$ The second expression is simply $3$. Now, to find the LCM, we take the highest powers of all the terms and combine them. Since $3$ and $2v(4v - 3)$ have no common factors other than $1$, the LCM will be: $\text{LCM}(2v(4v - 3), 3) = 2v(4v - 3) \times 3 = 6v(4v - 3)$ Thus, the correct answer is $6v(4v - 3)$, which corresponds to Option D in the image.

Solution to Question 6:

We are tasked with finding the LCM of $(b+6)(b+2)$ and $4(b+2)$.

• The first expression is $(b+6)(b+2)$.
• The second expression is $4(b+2)$.

Since both expressions contain the factor $(b+2)$, the LCM will take the highest powers of all factors. The LCM will be: $\text{LCM}((b+6)(b+2), 4(b+2)) = 4(b+6)(b+2)$ Thus, the correct answer is Option C: $4(b+2)(b+6)$.

Solution to Question 7:

We need to find the LCM of $(x+3)$ and $(x-3)$.

• The first expression is $(x+3)$.
• The second expression is $(x-3)$.

Since these two terms share no common factors, the LCM will simply be the product of both terms: $\text{LCM}((x+3), (x-3)) = (x+3)(x-3)$ This is a difference of squares, which simplifies to: $(x+3)(x-3) = x^2 - 9$ Thus, the correct answer is Option E: $x^2 - 9$.

Would you like further details on any of the solutions, or do you have any questions? Here's a list of related questions to expand your understanding:

1. How do you find the LCM of polynomials with more complex factors?
2. What happens if the expressions share common factors?
3. How can factoring help simplify finding the LCM?
4. Can you apply these methods to higher degree polynomials?
5. What is the role of the greatest common divisor (GCD) when finding LCM?

Tip: When finding the LCM of polynomials, always factor each polynomial completely first to make identifying common factors easier.