When m is an integer, the solution of the equation 12mx − 53 = 12 (x − 43) is a positive integer?

When m is an integer, the solution of the equation 12mx − 53 = 12 (x − 43) is a positive integer?

If we solve the equation 12mx − 53 = 12 (x − 43), remove the denominator, we get 3mx-10 = 3 (x-43), remove the bracket, we get 3mx-10 = 3x-4, transfer the term and merge the similar terms, we get x (m-1) = 2, the coefficient is 1, we get x = 2m − 1, ∵ the solution of the equation is a positive integer, ∵ x > 0 and is a positive integer, ∵ 2m − 1 > 0 and M is a positive integer, ∵ M-1 is a positive divisor of 2, that is, M-1 = 1 or 2, ∵ M = 2 or 3