The processes are allocated to the suitable resource node according to the resource availability in hypercube based clusters using a least cost allocation algorithm. In the clusters, nodes are arranged in hypercube structure, using a small world theory. The main goal is to find the appropriate resource with minimum search cost and maximum search efficiency. The frame work, which is proposed, follows a linear programming model for grid resource allocation. It organizes resource elements into a set of hyper cubed overlay networks. Within this frame work, an algorithm is defined with request forwarding strategy. This strategy decides to which node a request to be forwarded. The resource availability in hypercube based clusters are discovered and allocated the request to the appropriate alive node using Prioritized Least Cost Method Algorithm (PLCM). The proposed PLCM Algorithm aims at minimum cost. The result shows that the proposed PLCM Algorithm, when compared with Least Cost Method (LCM) reduces the processing cost, satisfies the user demand, improves the resource utilization and balances the load across the grid environment.