2020 CIME II Problems/Problem 12
Note that the and its iterations are all divisible by 180. This implies that 2 of are divisible by 4, 2 are divisible by 9 and 2 are divisible by 5.
Next we note that iterations are 180,,. This implies that or must have an additional factor of 2 and or must have an additional factor of 3. The sum is minimized if d=2 and e=3 and f=1.