We study universal bosonic few-body systems within the framework of effective field theory at leading order (LO). We calculate binding energies of systems of up to six particles and the atomdimer scattering length. Convergence to the limit of zero-range two-and three-body interactions is shown, indicating that no additional few-body interactions need to be introduced at LO. Generalizations of the Tjon line are constructed, showing correlations between few-body binding energies and the binding energy of the trimer, for a given dimer energy. As a specific example, we implement our theory for 4 He atomic systems and show that the results are in surprisingly good agreement with those of sophisticated 4 He-4 He potentials. Potential implications for the convergence of the EFT expansion are discussed.

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