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In this paper we identify the structure of complex finite-dimensional Leibniz algebras with associated Lie algebras $sl_2^1\oplus sl_2^2\oplus \dots \oplus sl_2^s\oplus R,R$ is a solvable radical. The classifications of such Leibniz algebras in the cases and have been obtained. Moreover, we classify Leibniz algebras with $L/I\cong sl_2^1\oplus sl_2^2I=id<[x,x] \ | \ x\in L>.$

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