Tur\'an numbers of vertex-disjoint cliques in $r$-partite graphs

For two graphs $G$ and $H$, the Tur'{a}n number $ex(G,H)$ is the maximum number of edges in a subgraph of $G$ that contains no copy of $H$. Chen, Li, and Tu determined the Tur'{a}n numbers $ex(K_{m,n},k{K}_2)$ for all $k\ge 1$ [7]. In this paper we will determine the Tur'{a}n numbers $ex(K_{a_1,\dots ,a_r},k{K}_r)$ for all $r\ge 3$ and $k\ge 1$.