Recently, attracted by the abundant computation and networking resources in the cloud, an increased number of mobile media services have been hosted by the cloud computing platforms. These mobile media clouds (MMCs) run hundreds of thousands of servers and consume megawatts of power with massive carbon emission. Virtualization is adopted to allocate resources elastically from a shared resource pool. Therefore, effective virtual machine (VM) consolidation is of paramount importance to reduce energy consumption. We especially focus on applications with different resource (e.g., CPU, memory, network) demands. In this paper, we formulate this problem as a mixed integer linear programming (MILP) problem. We prove that the optimal energy efficiency can be obtained for a homogeneous cloud. Based on this analytical result, we develop an approximation algorithm for VM consolidation and placement which jointly considers CPU and network constraints. Through extensive simulations, we validate the effectiveness of the proposed algorithm.