Why LC filters are not used in PLL structures?

According to my research In all PLL structures different orders of RC filters are used. I am curious that why an LC filter is not used ? Isn't it less noisy ?

Thanks.

I guess to realize LP filter in hundreds of kHz using LC, the component values (or the size) is big.

No, that is not the reason.
An LC low pass by definition is of second order. Together with the pole of the VCO this would bring the loop to instability.
Therefore, only a FIRST order lowpass is allowed, which - in addition - has a zero for a frequency somewhat above the low pass pole. Alternative: PI - element.
In most cases it is ncessary to increase damping with another pole which is located above the unity gain frequency of the loop gain applying the small signal loop model. (Therefore, some people speak of a second order lowpass).
Regards
LvW

No, that is not the reason.
An LC low pass by definition is of second order. Together with the pole of the VCO this would bring the loop to instability.
Therefore, only a FIRST order lowpass is allowed, which - in addition - has a zero for a frequency somewhat above the low pass pole. Alternative: PI - element.
In most cases it is ncessary to increase damping with another pole which is located above the unity gain frequency of the loop gain applying the small signal loop model. (Therefore, some people speak of a second order lowpass).
Regards
LvW