  Lagrangian cobordism induces a preorder on the set of Legendrian links in any
contact 3-manifold. We show that any finite collection of null-homologous
Legendrian links in a tight contact 3-manifold with a common rotation number
has an upper bound with respect to the preorder. In particular, we construct an
exact Lagrangian cobordism from each element of the collection to a common
Legendrian link. This construction allows us to define a notion of minimal
Lagrangian genus between any two null-homologous Legendrian links with a common
rotation number.
