In this work we study period control of the mammalian cell cycle via coupling with the cellular clock. For this, we make use of the oscillators' synchronization dynamics and investigate methods of slowing down the cell cycle with the use of clock inputs. Clock control of the cell cycle is well established via identified molecular mechanisms, such as the CLOCK:BMAL1-mediated induction of the wee1 gene, resulting in the WEE1 kinase that represses the active form of MPF (mitosis promoting factor), the essential cell cycle component. To investigate the coupling dynamics of these systems, we use previously developed models of the clock and cell cycle oscillators and center our studies on unidirectional clock → cell cycle coupling. Moreover, we propose an hypothesis of a Growth Factor (GF)-responsive clock, involving a pathway of the non-essential cell cycle complex cyclin D/CDK4. We observe a variety of rational ratios of clock to cell cycle period, such as: 1:1, 3:2, 4:3 and 5:4. Finally, our protocols of period control are successful in effectively slowing down the cell cycle by the use of clock modulating inputs, some of which correspond to existing drugs.