What is the LCM of x^3 + 8, x^2 + 5x + 6 and x^3 + 4x^2 + 4x

What is the LCM of x3 + 8, x2 + 5x + 6 and x3 + 4x2 + 4x?

  1. x (x + 2)2 (x + 3) (x2 - 2x + 4)
  2. x (x - 2)2 (x - 3) (x2 + 2x + 4)
  3. (x + 2)2 (x + 3) (x2 - 2x + 4)
  4. (x - 2)2 (x - 3) (x2 - 2x + 4)

Answer

x3 + 8 = (x + 2)(x2 - 2x + 4)

x2 + 5x + 6 = (x + 2)(x + 3)

x3 + 4x2 + 4x = x(x2 + 4x + 4) = x(x + 2)2

LCM = x (x + 2)2 (x + 3) (x2 - 2x + 4)

The correct option is A.