GCD_ADD

Returns the greatest common divisor of two or more integers. (inc negative numbers)

link - wiki.documentfoundation.org/Documentation/Calc_Functions/GCD_EXCEL2003 
link - help.libreoffice.org/latest/en-US/text/scalc/01/04060106.html 

Microsoft Excel

The GCD function in Excel returns an error if any of the arguments are negative values.

GCD(-8, 16) = #NUM! 

LibreOffice Calc

The GCD function in LibreOffice returns a value if any of the arguments are negative values.

GCD(-8; 16) = -8 

The GCD_ADD or GCD_EXCEL2003 function in LibreOffice provides an identical function to Excel.

GCD_ADD(-8; 16) = #NUM! 
GCD_EXCEL2003(-8; 16) = #NUM!