Abstract: The desire in this research is to design a Mealy state digital machine using NAND gates only to compute the GCD of any two numbers. In the design, state selection, input variable, output variable definition and output assignment to ensure accurate result are considered. The method employed in this design is a classical method of digital design that utilized purely the State diagram, State Table, Excitation Table and Kanaugh Map (K-Map). The GCD of the numbers (40, 24) was obtained as 8. Although, the machine is capable of computing the GCD of any number provided the input is stated correctly.