Business cycles appear highly synchronized across countries. To understand this empirical phenomenon, I develop a multi-country international real business cycle model with international trade that offers several potential explanations: shocks to TFP, demand, leisure, investment, economic sectors, and bilateral trade. These shocks fully account for movements in gross domestic product and trade shares, completely describing the data during 1992-2014. Calibrating the model to a panel of developed (G7) countries, I find that openness to trade and the volatility of bilateral trade flows, which are manifested in bilateral trade shocks, are essential in synchronizing international business cycles. In contrast, other correlated country-specific shocks play relatively minor roles. This suggests that economic integration through trade has been the primary driver of the co-movement of business cycles internationally. I use my model to also address the \textit{trade co-movement puzzle}, which states that international real business cycle models should be predicting a much stronger link between trade and the correlation of business cycles. Once we account for the dynamics of the decline in trade costs and the volatility of bilateral trade flows, IRBC models do indeed predict a strong link between trade and business cycle co-movement. My finding suggests that more research on the dynamics of trade shocks is crucial when studying cross-country business cycle synchronization.