Please some one explain why the gain margin has to be less than the phase margin for the stable system?
You mean, less in the numbers used? Phase margin is in degrees, while gain margin is in dB (or magnitude ratio). Yes the dB figure will typically be smaller than the degrees of phase margin. If gain margin were expressed as a magnitude ratio, would that figure also be less than phase margin? Probably not.
I think your question is not clear me. There is no term "gain margin frequency" or "phase margin frequency".
It is "gain cross-over frequency(wg)" and "phase cross-over frequency(wp)"
See this bode plot. It is also a stable system but wg>wp.
It is not true wg
https://www.electrical4u.com/bode-plot-gain-margin-phase-margin/
http://in.mathworks.com/help/control/ref/margin.html?requestedDomain=in.mathworks.com
If you are referring to cross-over frequencies, your statement is true in a specific case. If you have a system such that the Amplitude ratio is a monotonically decreasing function of frequency, then if your gain cross-over frequency is smaller than phase cross-over frequency, your system will be stable. However, it is not true in general.