Final answer:
Dropbox is the lightweight document management system that allows cloud storage of documents, providing access and sharing capabilities with real-time updates.
Step-by-step explanation:
The lightweight document management system that allows you to store documents in the cloud is B) Dropbox. This platform is designed specifically for file storage and synchronization. Users can save their files online and synchronize them with their devices, making it easy to access and share documents with others. Real-time updates ensure all users see the most recent version of a document. While SharePoint also offers cloud storage, it is more complex and oriented towards enterprise collaboration. Trello and Asana are task and project management platforms, not primarily focused on document storage.