To find the Least Common Denominator (LCD) of the rational expressions given, we need to look at the denominators in each fraction.

The rational expressions provided are: $\frac{2}{x+8} \quad \text{and} \quad \frac{16}{x-8}$

Step 1: Identify the Denominators

The denominators are $x + 8$ and $x - 8$.

Step 2: Determine the LCD

Since the denominators are distinct linear factors $(x + 8)$ and $(x - 8)$, the LCD will be the product of these two factors: $\text{LCD} = (x + 8)(x - 8)$

Step 3: Simplify if Needed

This expression, $(x + 8)(x - 8)$, does not simplify further in this context, so the LCD remains: $\text{LCD} = (x + 8)(x - 8)$

In factored form, the LCD of these rational expressions is $(x + 8)(x - 8)$.

Would you like further details on how to use this LCD to perform operations on these fractions or have any other questions?

Here are five related questions for further exploration:

1. How do you add rational expressions with different denominators?
2. What is the importance of factoring when finding the LCD of rational expressions?
3. How do you simplify complex rational expressions after finding the LCD?
4. Can the LCD be expressed in simplified form if both denominators share common factors?
5. How would the LCD change if the denominators were quadratic expressions instead of linear?

Tip: Always factor each denominator fully when finding the LCD; this makes it easier to identify common and unique factors.