Why is money divisible? To explore this question we introduce a mismatch problem into search-theoretic models of monetary exchange. We use alternative assumptions about the divisibility of goods and money and the ability of agents to use lotteries on money. Our framework potentially generates three types of inefficiencies: the no-trade inefficiency where no trade takes place even though it would be socially efficient to trade; the too-much-trade and too-little-trade inefficiencies where the quantities produced and exchanged are either larger or smaller than what the solution to a social planner's problem would dictate. It is shown that while the no-trade and the too-much-trade inefficiencies are caused by the indivisibility of money, the too-little-trade inefficiency is due to the impatience of the traders and the time-consuming exchange process. Furthermore, we find that the lottery model with indivisible money and divisible goods is qualitatively similar to the divisible money and divisible goods model.