With the fast growth of the demand for Cloud computing services, the Cloud has become a very popular platform to develop distributed applications. Features that in the past were available only to big corporations, like fast scalability, availability, and reliability, are now accessible to any customer, including individuals and small companies, thanks to Cloud computing. In order to place an application, a designer must choose among VM types, from private and public cloud providers, those that are capable of hosting her application or its parts using as criteria application requirements, VM prices, and VM resources. This procedure becomes more complicated when the objective is to place large component based applications on multiple clouds. In this case, the number of possible configurations explodes making necessary the automation of the placement. In this context, scalability has a central role since the placement problem is a generalization of the NP-Hard multi-dimensional bin packing problem. In this paper we propose efficient greedy heuristics based on first fit decreasing and best fit algorithms, which are capable of computing near optimal solutions for very large applications, with the objective of minimizing costs and meeting application performance requirements. Through a meticulous evaluation, we show that the greedy heuristics took a few seconds to calculate near optimal solutions to placements that would require hours or even days when calculated using state of the art solutions, namely exact algorithms or meta-heuristics.