Visualize the Euclidean algorithm again
Charcoal, 30 bytes

ＮδＮγＦβ¿×γδ«ＵＯγδι¿‹γδＡ⁻δγδＡ⁻γδγ


Try it online! Explanation:

Ｎδ      Input d
Ｎγ      Input g
Ｆβ      For i In ['a' ... 'z']
 ¿×γδ«   If g * d
  ＵＯγδι   Oblong g, d, i
  ¿‹γδ    If g &lt; d
   Ａ⁻δγδ   d = d - g
   Ａ⁻γδγ   Else g = g - d


Annoyingly Charcoal's Oblong command won't take 0 for a dimension, which costs me 4 bytes. The other approach would be to loop while g * d, but then I couldn't work out how to iterate over b (which is predefined to the lowercase letters).