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A rainbow geodesic in an edge-colored graph G is a shortest path between a pair of vertices in which doesn’t contain color repetition. A local strong rainbow coloring of G is a coloring where there is a rainbow geodesic between each pair of vertices with a d-distance. The minimum number of colors required for a graph to have local strong rainbow coloring is called local strong rainbow connected number-d, written as lsrc_d. Suppose that graphs G and H are graphs of degree m and n, respectively. The corona product of G and H, G⊙H is a graph obtained by taking a copy of graph G and m copies of graph H, then each vertex of the i-th copy of H is connected to the i-th vertex of G. A complete graph of order n, K_n, is a graph which every pair vertex is adjacent. A wheel graph of order n, W_n, is a graph that contains a cycle of order n-1, and every vertex in the cycle is adjacent to a vertex. In this paper, we give the local strong rainbow connection numbers of K_m⊙K_n and K_m⊙W_n.