The equilibrium constant K for a reaction is related to the equilibrium constant of the corresponding reaction, whose equation is obtained by multiplying or dividing the equation for the original reaction by a small integer.
A+2B↔3C
K=[C]3[A][B]2
nA+2nB↔3nC
K′=[C]3n[A]n[B]2n
=([C]3[A][B]2)n
=Kn