Starting from the lattice Landau gauge gluon and ghost propagator data we use a sequence of Pade approximants, identify the poles and zeros for each approximant and map them into the analytic structure of the propagators. For the Landau gauge gluon propagator the Pade analysis identifies a pair of complex conjugate poles and a branch cut along the negative real axis of the Euclidean $p^2$ momenta. For the Landau gauge ghost propagator the Pade analysis shows a single pole at $p^2 = 0$ and a branch cut also along the negative real axis of the Euclidean $p^2$ momenta. The method gives precise estimates for the gluon complex poles, that agree well with other estimates found in the literature. For the branch cut the Pade analysis gives, at least, a rough estimate of the corresponding branch point.
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