A big thank you in advance for any help I can get.

My girlfriend bought what I think is a 2008 GT Zaskar Expert. (how can I tell for sure?)

It has a full Deore LX group. I need a middle chainring. It has a FC-M582 crankset. The Shimano part is Y1-FU 98020. Will another 32T with a 104mm BC work.