Balancing Chemical Equations

[ViktorKorobov]

I am using a matrix method for balancing a chemical equations. As a result, I get a vector x, which contains a set of non-integer numbers. Next, I need this vector is multiplied by a number Y, to obtain a set of integers. Total sum of these integers should be as small as possible.
How do I calculate the number Y?
See the picture and Mathcad worksheet in attach.

Viktor

[VladimirN]

In this case, not even enough constraints on the coefficients in the matrix "Coeffs".

[Fred_Kohlhepp · Accepted solution]

A brute force approach

[ViktorKorobov]

Thank you, Mr. Fred!
It really works!