In the proof of Gauss' Quadratic Reciprocity Law, a lemma known as Gauss' Lemma plays an important role. In this talk, we will introduce a lemma similar to Gauss' Lemma and show how this lemma can be used to prove the Quadratic Reciprocity Law. We will also prove the generalization of Jenkins' lemma that is closely related to Reciprocity Law for Jacobi symbol.