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In this work, the authors aimed to identify a potential correlation between the printability and crucial rheological characteristics of materials involved in fused deposition modeling (FDM) technology. In this regard, three different poly(lactide) acid (PLA)-based filaments (two commercially available (here called V-PLA and R-PLA) and one processed in a lab-scale extruder (here called L-PLA)) have been considered. Dynamic rheological testing, in terms of frequency sweep at five different temperatures (130, 150, 170, 190, and 210 °C), was performed. Rheological properties expressed in terms of viscoelastic moduli and complex viscosity curves vs. frequency, characteristic relaxation times, activation energy (Ea), zero shear viscosity (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>η</mi><mn>0</mn></msub></mrow></semantics></math></inline-formula>) and shear thinning index (n) were derived for each material. A characteristic relaxation time of around 0.243 s was found for V-PLA, a similar value (0.295 s) was calculated for R-PLA filaments, and a lower value of about an order of magnitude was calculated for L-PLA filament (~0.0303 s). The activation energy and shear thinning index resulted to be very comparable for all the filaments. On the contrary, V-PLA and R-PLA possessed a zero-shear viscosity (~10⁴ Pa*s at 170 °C) much higher than L-PLA (~10³ Pa*s). All the filaments were processed in a 3D printer, by attesting the effect of nozzle temperature (180, 190, and 210 °C, respectively) on printing process, and macroscopic shaping defects in printed objects. Final considerations allowed us to conclude that polymer relaxation time, zero-shear viscosity, and melt viscosity (affected by printing temperature) were critical parameters affecting the printing quality.