To find the least common multiple (LCM) of the two expressions:

1. $6v^8 x^2 u^3$
2. $9v^7 x^5$

Step-by-step Process:

1. Factor the coefficients:

• 6 = $2 \times 3$
• 9 = $3^2$

The LCM of 6 and 9 is $2 \times 3^2 = 18$.

2. Consider the variables with exponents:

• For $v$, the terms are $v^8$ and $v^7$. The LCM will take the highest power, so it will be $v^8$.
• For $x$, the terms are $x^2$ and $x^5$. The LCM will take the highest power, so it will be $x^5$.
• For $u$, there is $u^3$ in the first term and no $u$ in the second. So, the LCM will include $u^3$.

Final LCM:

The least common multiple is: $18v^8 x^5 u^3$

Let me know if you would like further clarification!

Here are 5 follow-up questions to expand this topic:

1. What is the greatest common divisor (GCD) of the two expressions?
2. How would the process differ if a variable had negative exponents?
3. Can the LCM be applied to fractional expressions?
4. How do you find the LCM of three or more algebraic expressions?
5. How is the LCM of algebraic expressions applied in solving equations?

Tip: Always take the highest power of each variable when finding the LCM of algebraic terms.