Change Data Capture (CDC) is the best option to meet the requirement. CDC is a type of streaming event that notifies subscribers of changes to Salesforce records, such as creation, update, delete, and undelete operations. By subscribing to CDC events for the course registration data, the LMS can receive real-time updates and sync with Salesforce. Streaming API is another type of streaming event that notifies subscribers of changes to Salesforce records that match a SOQL query. However, Streaming API has some limitations, such as not supporting all SOQL features and not capturing delete and undelete operations. Platform Event is a type of streaming event that delivers custom notifications within the Salesforce platform or from external sources. Platform Event is not suitable for this requirement because it is not tied to Salesforce records and requires custom logic to publish and subscribe. Outbound Message is a workflow action that sends SOAP messages with field values to designated endpoints. Outbound Message is not suitable for this requirement because it does not support complex data types, such as sObjects or collections.