Enter 0, -24, 36. Magnitudes are 0, 24 and 36, so gcd(0,24)=24 and then gcd(24,36)=12. Because the list contains zero, the released LCM convention returns zero.
The sign is not discarded silently
The normalized input list still displays -24, while the arithmetic columns use non-negative magnitudes. This separates what was entered from the divisibility convention used by the result.
Reproduce the complete fold
Enter the listed values in the same order. Read each pairwise row from left to right, then inspect the Euclidean equations until the remainder becomes zero. The final GCD must divide every input. If the list has no zero, the final LCM must be divisible by every input; if any input is zero, the released convention returns LCM zero.