Here's is simpler approach than the one that Nuno is proposing and you don't need to reference any dlls
var parentComponentid = ClientAdmin.GetTcmUri(component.Id, component.BluePrintInfo.OwningRepository.IdRef, null);
GetTcmUri
method is good for getting any TcmUris - just pass publication id you want your item in and Id of item in current publication. This way you can also find ID of a given item in particular child publication