Question

Find the LCM of 6x(x + 3)^2 (x – 2) and 9(x + 3)(x – 2)^2. Show your work.

54x(x + 3)^3(x – 2)^3

9x(x + 3)^2(x – 2)^2

18x(x + 3)^2(x – 2)^2

6x(x + 3)(x – 2)

Answer 1

Find the LCM by taking the highest power of each prime/variable factor that appears in either expression.

1. Numeric factors: 6 = 2·3, 9 = 3^2 → LCM(6,9) = 2·3^2 = 18.
2. x: appears as x^1 in the first and not at all in the second → include x^1.
3. (x+3): exponents are 2 (first) and 1 (second) → include (x+3)^2.
4. (x−2): exponents are 1 (first) and 2 (second) → include (x−2)^2.

Thus LCM = 18 x (x+3)^2 (x−2)^2.

This matches the third choice: 18x(x + 3)^2(x – 2)^2.