Let $X, Y$ be smooth, projective varieties, $L_X$ and $L_Y$ are very ample line bundles on $X$ and $Y$, respectively. If I understand correctly, $\mbox{pr}_1^*L_X \otimes \mbox{pr}_2^*L_Y$ is a very ample line bundle on $X \times Y$, where $\mbox{pr}_1, \mbox{pr}_2$ are the natural projections from $X \times Y$ to $X$ and $Y$, respectively. Is it possible to compute the degree of $\mbox{pr}_1^*L_X$ or $\mbox{pr}_2^*L_Y$ or $\mbox{pr}_1^*L_X \otimes \mbox{pr}_2^*L_Y$ with respect to the closed immersion defined by $\mbox{pr}_1^*L_X \otimes \mbox{pr}_2^*L_Y$ in terms of the degree of $L_X$ and $L_Y$ (computed with respect to the closed immersions given by $L_X$ and $L_Y$, respectively)?

Any reference/hint will be most welcome.