K2 space observations recently found that three super-Earths transit the nearby M dwarf K2-3. The apparent brightness and the small physical radius of their host star rank these planets amongst the most favourable for follow-up characterisations. The outer planet orbits close to the inner edge of the habitable zone and might become one of the first exoplanets searched for biomarkers using transmission spectroscopy. We used the HARPS velocimeter to measure the mass of the planets. The mass of planet $b$ is $8.4pm2.1$ M$_oplus$, while our determination of those planets $c$ and $d$ are affected by the stellar activity. With a density of $4.32^{+2.0}_{-0.76}$ $mathrm{g;cm^{-3}}$, planet $b$ is probably mostly rocky, but it could contain up to 50% water.
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