Multiplicity of Weil divisor on affine cone

Question

Let $D=(x, y)$ be a Weil divisor in the cone $A = k[x,y,z,w]/(xz-yw)$. I want to show that no multiplicity of $D$ is a Cartier divisor. This appears in Vakhil's book as an excersize, but he invokes some obscure technical lemma as a hint. I'm pretty sure it can be done more elementary, as I recall this excersize from the class, but forgot the solution and now I'm stuck.