Answer:
To find the LCM of the two expressions, we need to factor each expression completely and then take the product of the highest powers of each factor.
So, let's factor each expression:
6(x – 1)2(x + 2)(x – 3) = 2 × 3 × (x – 1) × (x – 1) × (x + 2) × (x – 3)
9(x – 1)(x + 2)2(x – 3) = 3 × 3 × (x – 1) × (x + 2) × (x + 2) × (x – 3)
Now, we can identify the highest powers of each factor.
The LCM will be the product of those highest powers:
LCM = 2 × 3 × 3 × (x – 1)2 × (x + 2)2 × (x – 3)
Therefore, the LCM of 6(x – 1)2(x + 2)(x – 3) and 9(x – 1)(x + 2)2(x – 3) is 54(x – 1)2(x + 2)2(x – 3).