A system and method are provided for synthesizing signal frequencies using a single reference clock and a primitive ratio of integers. The method accepts a plurality (k) of reference frequency values (fri), where 1≦i≦k, associated with a corresponding plurality of synthesized frequency values (foi). For each synthesized frequency value, a raw ratio of integers Nprawi and Dprawi is calculated, such that: f o i = Np raw i Dp raw i × f r i . A greatest common divisor (GCD) of Nprawi and Dprawi and a primitive ratio of integers Np i Dp i is found for each raw ratio of integers, such that: N p i = Np raw i GCD ⁡ ( Np raw i , Dp raw i ) ; and , ⁢ D p i = Dp raw i GCD ⁡ ( Np raw i , Dp raw i ) . Using the common clock frequency value (fcr), each primitive ratio of integers, each reference frequency value, and each GCD, a final ratio of integers Ncri and Dcri, C · ( N cr i D cr i ) , is calculated for each synthesized frequency value, where C is an integer value.