The GIlcm function computes and returns the first quadrant associate of a least common multiple of the Gaussian integers $x_1=a_1+\mathrm{I}{b}_1$, ..., $x_n=a_n+\mathrm{I}{b}_n$ where the $a_i$'s and the $b_i$'s are integers.  The first quadrant associate of a Gaussian integer is defined as ${\mathrm{I}}^{5-j}x$ where $x$ is a Gaussian integer and $j$ (1..4) is the quadrant containing $x$ (see GInormal).

$\mathrm{with}\left(\mathrm{GaussInt}\right)\:$

$\mathrm{GIlcm}\left(24\,12\right)$

$24$

$\mathrm{GIlcm}\left(-345+515\mathrm{I}\,1574+368\mathrm{I}\right)$

$3250+7400\mathrm{I}$