The value of a three digit number in base 10 will be from 10‌2to 10‌3 -1 . Similarly, the value of a three digit number in base 7 will be from 7‌2 to7‌3-1 . And the value of a three digit number in base 13 will be from 13‌2 to 13‌3- 1. So the common numbers are from 13‌2 to 7‌3 -1 . → 169 to 342 Hence, 174 such numbers would be there.