Why does LIGO have an arm length of few kilometers? Is the distance dependent on Gravitational Wave wavelength? Antennas for capturing radio waves need to have $\frac{\lambda}{2}$  length for optimum reception of signal. Does it imply LIGO arm length is $\frac{\lambda}{2}$ of Gravitational Wave it is trying to capture? 
 A: Pretty close. The effective LIGO arm length is 1600km (the light beam is reflected forth and back 400 times). LIGO is most sensitive at approx. 150Hz (advancedligo.mit.edu/summary.html), which would be a wavelength of 2000km... so the LIGO arms are approx. $\lambda /2$. The noise minimum depends on the noise spectrum, of course, so the sensitivity max. won't be exactly where one would expect it. 
A: The reason aerials are made with a particular length is because the interaction with the radio wave is a resonant process. Whether the transmission is AM or FM there is a central frequency. The radio aerial length is chosen so that this central frequency makes the electron density in the aerial resonate, which enhances the signal.
However gravity wave detection is not a resonant process so there is no reason why the arm length should bear any relation to the wavelength of the gravity wave. The arm length is chosen to maximise the signal and minimise noise.
A signal like the one detected causes a strain of around $10^{-21}$ so for example if the arms were one metre long they would change length by $10^{-21}$m, which is too small to be detected. make the arms a kilometre long and the length change becomes $1000 \times 10^{-21} = 10^{-18}$m, which is just detectable and indeed was detected.
But the longer you make the arms the harder (or more the the point the more expensive) it is to make them to the required precision. The length was chosen  to give the best sensitivity for the funds available.
