A magnetic skyrmion is a topological magnetization structure with a nanometric size and a well-defined swirling spin distribution, which is anticipated to be an essential building block for novel skyrmion-based device applications. We study the motion of magnetic skyrmions in multilayer synthetic antiferromagnetic (SAF) racetracks as well as in conventional monolayer ferromagnetic (FM) racetracks at finite temperature. There is an odd-even effect of the constituent FM layer number on the skyrmion Hall effect (SkHE). Namely, due to the suppression of the SkHE, the magnetic skyrmion has no transverse motion in multilayer SAF racetracks packed with even FM layers. It is shown that a moving magnetic skyrmion is stable even at room temperature (T = 300 K) in a bilayer SAF racetrack but it is destructed at T = 100 K in a monolayer FM racetrack. Our results indicate that the SAF structures are reliable and promising candidates for future applications in skyrmion-electronics and skyrmion-spintronics.