If $L/K$ is an extension of number fields, show that the integer ${\rm disc}(K)$ divides ${\rm disc}(L)$.

Question

If $L/K$ is an extension of number fields, show that the integer ${\rm disc}(K)$ divides ${\rm disc}(L)$.

My attempt :

We have a $\mathbb Z$-basis of $O_L$, then we can write down the basis elements of $O_K$ in terms of basis elements of $O_L$.But the matrix for this transformation is non-square. So I can not extract the determinant of this matrix.

Any help would be appreciated. Thanks in advance.