In LC circuit, if $X_L = X_C$ then $\omega = \frac{1}{\sqrt{LC}}$
$I_0 \infty$ , So $Z = \frac{E_0}{I_0} = 0$
As $\frac{1}{\sqrt{LC}}$ is the natural
frequency of $L C$ circuit, therefore for an $L C$ circuit if the frequency of applied $AC$ becomes equal to the natural frequency of an $AC$ circuit then the amplitude of current becomes infinite due to zero impedance.