Placement of Virtual Machines (VMs) on physical servers is a challenging area of research and has received considerable interest among researchers in the field of Cloud Computing. This paper focuses on the reduction of cost in placing a set of VMs considering the constraints of available cloud resources. We have proposed a polynomial time heuristic to place VMs satisfying the constraints with the objective of minimizing the number of active servers. When the number of VMs and servers are small, one restricted case of the problem can be solved optimally by forming an Integer Programming Problem (IPP). The performance of the proposed heuristics are evaluated considering different types of scenarios and it is observed that the maximum or average number of servers required by one of the proposed heuristics is nearly equal to that given by IPP based solution.