\( \Large x^{2}-4x = \left(x+2\right) \left(x-2\right) \) \( \Large \therefore L.C.M.\ of\ \left(x-2\right)\ and\ \left(x^{2}-4\right) \) = \( \Large 1 \times \left(x-2\right) \left(x+2\right) = x^{2}-4 \) and H.F.C. of \( \Large \left(x-2\right)\ and\ \left(x^{2}-4\right) = x-2 \)