Inside J Lo and A-Rod's New $15.3 Million NYC Apartment

J Lo and A-Rod's latest purchase screams they're in this thing for the long haul -- or maybe just the kick-ass views from their new home ... the first they've bought together.

We got these pics of the $15.3 million apartment the couple just snapped up, and the place is insane. It's 4,000 sq ft, 3 bedrooms, 4.5 bathrooms and that's all inside the 432 Park Avenue -- known as the world's tallest residential building.

We kinda got the feeling they'd get a pad together, since J Lo put her 26th Street penthouse on the market for $27 million last October. Btw, Alex and Jen didn't even break the bank, as far as this building is concerned. A Saudi retail mogul reportedly bought the penthouse for $87.7 million!