  We use the SMASH survey to obtain unprecedented deep photometry reaching down
to the oldest main sequence turn-offs in the colour-magnitude diagrams (CMDs)
of the Small Magellanic Cloud (SMC) and quantitatively derive its star
formation history (SFH) using CMD fitting techniques. We identify five
distinctive peaks of star formation in the last 3.5 Gyr, at $\sim $3, $\sim$2,
$\sim$1.1, $\sim $0.45 Gyr ago, and one presently. We compare these to the SFH
of the Large Magellanic Cloud (LMC) finding unequivocal synchronicity, with
both galaxies displaying similar periods of enhanced star formation over the
past $\sim$3.5 Gyr. The parallelism between their SFHs indicates that tidal
interactions between the MCs have recurrently played an important role in their
evolution for at least the last $\sim$3.5 Gyr, tidally truncating the SMC and
shaping the LMC's spiral arm. We show, for the first time, an SMC-LMC
correlated SFH at recent times in which enhancements of star formation are
localised in the northern spiral arm of the LMC, and globally across the SMC.
These novel findings should be used to constrain not only the orbital history
of the MCs but also how star formation should be treated in simulations.
