I would first use prime factorization to calculate the GCF and LCD. There are examples in the response I gave to Nicole and in the response that Leeanne and I gave to Debbie. I think that working directly from the prime factorization gives a solid foundation for both concepts.
There is a description of the ladder method in Example 3 on this page. In the response to Debbie referenced above one of the examples is worked out using the Euclidean Algorithm. This is probably the best method to use if the numbers are large enough that prime factorization becomes difficult.