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Nevertheless, only a mere fraction of the small planets detected by<jats:italic>Kepler<\/jats:italic>and K2 have precise mass measurements, which are mandatory to constrain their composition. We aim to characterise the planets that orbit the relatively bright star K2-138. This system is dynamically particular as it presents the longest chain known to date of planets close to the 3:2 resonance. We obtained 215 HARPS spectra from which we derived the radial-velocity variations of K2-138. Via a joint Bayesian analysis of both the K2 photometry and HARPS radial-velocities (RVs), we constrained the parameters of the six planets in orbit. The masses of the four inner planets, from b to e, are 3.1, 6.3, 7.9, and 13.0<jats:italic>M<\/jats:italic><jats:sub>\u2295<\/jats:sub>with a precision of 34, 20, 18, and 15%, respectively. The bulk densities are 4.9, 2.8, 3.2, and 1.8 g cm<jats:sup>\u22123<\/jats:sup>, ranging from Earth to Neptune-like values. For planets f and g, we report upper limits. 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