<p>The variants of FETI (finite element tearing and interconnecting) based domain decomposition methods are well-established, massively parallel algorithms for solving huge linear systems arising from the discretization of elliptic partial differential equations. Here, we adapt the FETI method for solving the large least squares problems associated with inconsistent systems of linear equations arising from the discretization of elliptic partial differential equations. We briefly review the symmetric least squares problems and the FETI method, explain how FETI can find the least squares solution, prove the optimal rate of convergence, and present the results of numerical experiments demonstrating the efficiency of the proposed method in solving the least squares problem defined by the Poisson equation with inconsistent Neumann conditions.</p>