Ok, so take the reaction A(g) --> 2B(g).
Kc is given by p(B)^2/p(A) where p(B) denotes the partial pressure of B.
If you increase the pressure, the partial pressures of B and A both change - A will increase, where B will decrease (according to Le C. - equilibrium shifts left, more A is produced, so its partial pressure increases, where B's decreases.)
But the effects of the changes of B and A cancel each other out, leaving Kc the same. So even though the equilibrium does shift, the value of the equilibrium constant remains the same.
Hope this is helps :-)