The -symmetry reduction method and Jacobi last multipliers

For nth order ordinary differential equations, it is studied the role of a Jacobi last multiplier (JLM) in the reduction processes that arise from the existence of either a k parametric symmetry group or a λ -symmetry. For the reduction derived from a λ -symmetry, JLMs are inherited as integrating factors of the auxiliary equations. Several ways that have appeared recently to solve the determining equations of the λ -symmetries are also analysed. Two examples illustrate the combined use of λ -symmetries and JLMs to obtain the complete solution of the equations.