Kc(equilibrium constant) and Kp
From the ideal gas equation, we get
$$PV=nRT \implies P=\frac{n}{V}RT=cRT$$
where $c$ represents the concentration.

Consider an arbitrary reaction
$$n_AA\rightarrow n_BB$$

$$K_c=\frac{c_B^{n_B}}{c_A^{n_A}}$$
$$K_p=\frac{P_B^{n_B}}{P_A^{n_A}}=\frac{(c_BRT)^{n_B}}{(c_ART)^{n_A}}=K_c \times (RT)^{\Delta n}$$

Most probably, the reaction you are talking about has $\Delta n=0$.