KöMaL 2016 K503

A mathematics teacher was having fun on the 1st of April. During that day, he interpreted any written numbers and operations as representations in the base equal to the whole hour of the time instant the operation was carried out. (For example, at 32 minutes past 1 p.m., that is, at 13:32, he assumed that numbers were represented in base 13.) When he first carried out a multiplication, he got 181 as a result. One hour later, he carried out the multiplication written down with the very same digits, and got 180. Two additional hours after the second multiplication, he added the numbers 180 and 181, and obtained 341. What was the original multiplication (written down with the original digits)?