Ok so I'm flying the F1 C172 on approach to KLGA. I'm about 10 miles out and at 2500 feet and lined up with ILS 04 (ILGA). I hit the APR on the autopilot. It immediately locks on to the localizer but for some reason it just does not seem to lock on to the glideslope. The autopilot does indicate APR GS so what am I doing wrong? Thank you.

The plate shows at 2700 DME 11.1 (LGA VOR) to DME 9.7 the GS intersects, so you should be OK at 2500 with the GS indicator showing it is above you. Be sure you engage APPR with the GS still above you so as it passes through the center lock on can occur.You also must be at the correct IAS for your weight and flaps, not too fast, or it may not lock on. At least that's been my experience. The aircraft performance must be such at that time that it is within the limits of autopilot control (not outside pitch trim range).Be sure you are on 110.5 and the ID reads I-LGA. The DME reading would be on your NAV 2 set to 113.1 LGA VOR.In the real world if they even allow a C172 in there to expedite traffic you'd be flying most of the final possibly with no flaps at near cruise slowing maybe enough at just pass the LOM 4 miles out from the threshold to flaps 1 speed as you cross the threshold just above that flaps 1 stall speed so you don't float that far. At a busy time you have to use a fast final for an airport like that, especially without parallel runways.