We present the time variability properties of a sample of six blazars, AO 0235+164, 3C 273, 3C 279, PKS 1510-089, PKS 2155-304, and 3C 454.3, at optical-IR as well as gamma-ray energies. These observations were carried out as a part of the Yale/SMARTS program during 2008-2010 that has followed the variations in emission of the bright Fermi-LAT-monitored blazars in the southern sky with closely-spaced observations at BVRJK bands. We find the optical/IR time variability properties of these blazars to be remarkably similar to those at the gamma-ray energies. The power spectral density (PSD) functions of the R-band variability of all six blazars are fit well by simple power-law functions with negative slope such that there is higher amplitude variability on longer timescales. No clear break is identified in the PSD of any of the sources. The average slope of the PSD of R-band variability of these blazars is similar to what was found by the Fermi team for the gamma-ray variability of a larger sample of bright blazars. This is consistent with leptonic models where the optical-IR and gamma-ray emission is generated by the same population of electrons through synchrotron and inverse-Compton processes, respectively. The prominent flares present in the optical-IR as well as the gamma-ray light curves of these blazars are predominantly symmetric, i.e., have similar rise and decay timescales, indicating that the long-term variability is dominated by the crossing time of radiation or a disturbance through the emission region rather than by the acceleration or energy-loss timescales of the radiating electrons. In the blazar 3C 454.3, which has the highest-quality light curves, the location of a large gamma-ray outburst during 2009 December is consistent with being in the jet at ~18 pc from the central engine. This poses strong constraints on the models of high energy emission in the jets of blazars.
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