L, C and R represent the physical quantities inductance, capacitance, and resistance, respectively. The combinations which have the dimensions of frequency are

RC has the dimensions of time, so $\frac{1}{\mathrm{RC}}$ will have the dimensions of frequency. Similarly, $\frac{L}{R}$ has the dimensions of time, so $\frac{R}{L}$ will have will have the dimensions of frequency 

Now, $\frac{1}{\sqrt{\mathrm{LC}}}=\frac{1}{\sqrt{\frac{\mathrm{L}}{\mathrm{R}}\mathrm{RC}}}=\frac{1}{\sqrt{\mathrm{T}\times \mathrm{T}}}=\frac{1}{\mathrm{T}}$ is the dimensions of frequency