In this article, we address the problem of reproducibility of the blocked LU factorization on GPUs due to cancellations and rounding errors when dealing with floating-point arithmetic. Thanks to the hierarchical structure of linear algebra libraries, the computations carried within this operation can be expressed in terms of the Level-3 BLAS routines as well as the unblocked variant; the latter is correspon-dently built upon the Level-1/2 BLAS kernels. In addition, we strengthen numerical stability of the blocked LU factorization via partial row pivoting. Therefore, we propose a double-layer bottom-up approach for ensuring reproducibility of the blocked LU factorization and provide experimental results for its underlying blocks.