Distributed systems have problems with downtime, data loss during malfunctions, scalability and efficient use of computing resources. At the same time in the learning and training process, the use of a distributed system has the advantage of data processing: storage of information about students, construction of training courses, verification of passed material, etc. The problems of scaling and efficient use of resources in distributed learning management systems are investigated in this research. Cloud platforms for hosting the system, such as Amazon Web Services, Microsoft Azure, Google Cloud Platform and DigitalOcean are reviewed. Problems and features of a scalability in cloud computing are discussed. Methods, scaling and load balancing algorithms for the efficient use of computing resources are proposed. According to the list of advantages, the DigitalOcean platform was selected for the investigation. DigitalOcean provides cloud servers that can be used for quick creation of the new virtual machines for the projects. These servers allow to fully control the web hosting environment at the same time that the user pays only for the resources used. The main goal of DigitalOcean is to use a solid-state drive (SSD) to create a user-friendly platform that will allow clients to migrate projects to and from the cloud, increasing productivity with high speed and efficiency. As a result of analyzing information on existing technologies, approaches and methods for using cloud platforms in distributed systems, they have been applied to develop a solution to reduce downtime for a distributed adaptive Learning Management System (LMS). It is concluded that the use of cloud platforms for the construction of distributed LMS a practice that allows to use only the required amount of computing capacity. It is proven, that the implementation of the proposed solution into the work of adaptive LMS will improve its efficiency by reducing the time of the content delivering.