Multiple cores can utilize the same Management Gateway Appliance. The same is not true in reverse (each core can use only one Gateway Appliance).
Your scenario (mutliple cores, one Appliance) should work fine.
Thanks a lot for your rply.
Can you brief me more about this scenario(Diffrent Core Server utilize single LMG). I mean how the setting will be?
There's really nothing to it. Set up each core how you would, but it just happens to point to the same Gateway Appliance. The Appliance will hold the certificates from both cores without a problem. It's really no different than setting up a single core to an Appliance.