Final answer:
The highest power of x that appears in both monomials is x^2. Therefore, the LCM is 8x^2 * 12x^2 = 96x^4. So, the correct answer is 96x^4. The least common multiple (LCM) of the monomials 8x² and 12x³ is 96x⁴.
Step-by-step explanation:
The least common multiple (LCM) of two monomials can be found by finding the highest power of each variable that appears in both monomials, and then multiplying them together.
In this case, the variables are x.
The highest power of x that appears in both monomials is x^2.
Therefore, the LCM is 8x^2 * 12x^2 = 96x^4.
So, the correct answer is 96x^4.