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We study tight bounds and fast algorithms for LCLMs of several lineardifferential operators with polynomial coefficients. We analyze the arithmeticcomplexity of existing algorithms for LCLMs, as well as the size of theiroutputs. We propose a new algorithm that recasts the LCLM computation in alinear algebra problem on a polynomial matrix. This algorithm yields sharpbounds on the coefficient degrees of the LCLM, improving by one order ofmagnitude the best bounds obtained using previous algorithms. The complexity ofthe new algorithm is almost optimal, in the sense that it nearly matches thearithmetic size of the output.

Fast Computation of Common Left Multiples of Linear Ordinary Differential Operators