Mathematics Using DNA: Performing GCD and LCM on a DNA Computer

Abstract

DNA Computing has attracted the eyes of many researchers since its inception in 1996. It over-performs conventional computer due to its inherent massively parallelism nature in case of the computationally hard problems. But to make DNA computer usable in general, it needs to be able to perform important mathematical calculations. Example of such mathematical functions include finding greatest common divisor (GCD) and least common multiple (LCM), which are interrelated as their multiplication results in the multiplication of the two numbers. GCD can be found on conventional machine using Euclid's Algorithms that takes number of steps approximately proportional to the natural logarithm of the larger number. LCM is found by dividing GCD from the multiplication of two numbers. GCD and LCM can also be found using prime factorization of the two numbers, but this itself is computationally hard. In this work, at first LCM has been found using DNA molecule at constant time. Then GCD can be found by multiplying the two numbers and dividing by LCM onconventional machine. So, GCD and LCM can be found using constant number of operations. Experimental feasibility of the bio-molecular operations has also been described. This work is expected to be important bridge to make DNA computing applicable in the area of numerical mathematics.