I have a koi fish pond with about 14 to 15 inch (around 37 cm) koi. The neighborhood kid threw a piece of gum in the pond and one of my koi ate it; how harmful is this?
If the water is cold then it can be a problem, chewing gum will start to get soft at temperatures above 20 °C.
So if the water is warmer than 20 °C it will pass through your fish - slowly, but it will pass. The warmer the water, the faster it goes.
If your water is cold you might have a problem, but not always as the fish are able to regurgitate and spit it out
I have seen koi eat and spit out objects that have been in my pond, like styrofoam and plastic pieces, sometimes after quite some time.
Your koi are large, so I do not think they will have any problems passing the gum.