Archimedes' Cattle Problem

Have you ever solved the Archimedes' Cattle Problem?




It is a problem in 2 parts .. this is the first part that need to be solve:




The cattle of the Sun were divided in 4 herds of different color. (White, Black, Yellow and Dappled)


- The number of white bulls was equal to (1/2 + 1/3) the number of black bulls plus the total number of yellow bulls


- The number of black bulls was (1/4 + 1/5) the number of dappled bulls plus the total number of yellow bulls


- The number of dappled bulls was (1/6 + 1/7) the number of white bulls plus the total number of yellow bulls


- The number of white cows was (1/3 + 1/4) the number of cattle in the black herd


- The number of black cows was (1/4 + 1/5) the number of cattle in the dapple herd


- The number of dappled cows was (1/5 + 1/6) the number of cattle in the yellow herd


- The number of yellow cows was (1/6 + 1/7) the number of cattle in the white herd


What is the minimum number of cattle of the Sun (The smallest solution for the sum of cattle in the 4 herds)

0

Well, let assume that 0 is not a herd