Market fragmentation across multiple Automated Market Makers (AMMs) creates inefficiencies such as costly arbitrage, unnecessarily high slippage and delayed incorporation of new information into prices. These inefficiencies raise trading costs, reduce liquidity provider profits, and degrade overall market efficiency. To address these issues, we propose a modification of the Constant Product Market Maker (CPMM) pricing mechanism, called the Global Market Maker (GMM), which aggregates liquidity information from all AMMs to mitigate these inefficiencies. Through theoretical and numerical analyses, we demonstrate that the GMM enhances profits for both AMMs and traders by eliminating arbitrage opportunities. Additionally, it reduces the profitability of sandwich attacks and minimizes impermanent losses.