Blazars are known for their energetic multiwavelength flares from radio wavelengths to high-energy $gamma$-rays. In this work, we study radio, optical, and $gamma$-ray light curves of 145 bright blazars spanning up to 8~yr, to probe the flaring activity and interband correlations. Of these, 105 show $>1sigma$ correlations between one or more wavebands, 26 of which have a $>3sigma$ correlation in at least one wavelength pair, as measured by the discrete correlation function. The most common and strongest correlations are found between the optical and $gamma$-ray bands, with fluctuations simultaneous within our $sim 30$~d resolution. The radio response is usually substantially delayed with respect to the other wavelengths with median time lags of $sim 100$--160~d. A systematic flare identification via Bayesian block analysis provides us with a first uniform sample of flares in the three bands, allowing us to characterise the relative rates of multiband and orphan flares. Multiband flares tend to have higher amplitudes than orphan flares.
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