Context. Luminous Blue Variables (LBVs) are thought to be in a transitory phase between O stars on the main-sequence and the Wolf-Rayet stage. Recent studies suggest that they might be formed through binary interaction. Only a few are known in binary systems but their multiplicity fraction is uncertain. Aims. This study aims at deriving the binary fraction among the Galactic (confirmed and candidate) LBV population. We combine multi-epoch spectroscopy and long-baseline interferometry. Methods. We use cross-correlation to measure their radial velocities. We identify spectroscopic binaries through significant RV variability (larger than 35 km/s). We investigate the observational biases to establish the intrinsic binary fraction. We use CANDID to detect interferometric companions, derive their parameters and positions. Results. We derive an observed spectroscopic binary fraction of 26 %. Considering period and mass ratio ranges from Porb=1 to 1000 days, and q = 0.1-1.0, and a representative set of orbital parameter distributions, we find a bias-corrected binary fraction of 62%. From interferometry, we detect 14 companions out of 18 objects, providing a binary fraction of 78% at projected separations between 1 and 120 mas. From the derived primary diameters, and the distances of these objects, we measure for the first time the exact radii of Galactic LBVs to be between 100 and 650 Rsun, making unlikely to have short-period systems. Conclusions. This analysis shows that the binary fraction among the Galactic LBV population is large. If they form through single-star evolution, their orbit must be initially large. If they form through binary channel that implies that either massive stars in short binary systems must undergo a phase of fully non-conservative mass transfer to be able to sufficiently widen the orbit or that LBVs form through merging in initially binary or triple systems.
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