Find the number of positive integers that are divisors of at least one of 1010,1212 , and 1515.
Divisors of 10^10 =2^10 x 5^10 = 11 x 11 =121
Divisors of 12^12 =2^24 x 3^12 = 25 x 13 =325
Divisors of 15^15 =3^15 x 5^15 = 16 x 16 =256
121 + 325 + 256 =702 divisors of all 3 numbers. However, I counted 34 as duplicates. If we remove these 34 duplicates, then we have: 702 - 34 =668 divisors of at least one of your 3 numbers (10^10, 12^12, 15^15).