The utility model discloses an engine and an exhaust manifold of the engine. The exhaust manifold of the engine comprises at least two branch manifolds, wherein at least two locating holes are formed in each branch manifold, and are used in cooperation with corresponding locating holes formed in the engine, and every two adjacent branch manifolds are connected in an inserted mode, and are in clearance fit; in addition, one locating hole of at least one of the branch manifolds is provided with a small-diameter hole, the hole diameter of each small-diameter hole is smaller than the hole diameters of other locating holes so that the branch manifold can rotate relative to the adjacent branch manifold around the axis of the corresponding small-diameter hole under the action of the gravity, and line sealing can be formed. Due to the facts that the small-diameter holes are formed in the branch manifolds of the exhaust manifold, each branch manifold can rotate relative to the corresponding adjacent branch manifold in the process that the branch manifolds are installed on the engine, line sealing can be formed, harmful liquid is prevented from leaking, an annular groove and a sealing ring do not need to be arranged, and the cost is reduced; in addition, the branch manifolds are in clearance fit, and assembly and disassembly are convenient.