**784913526**

78 84 49 91 13 35 52 26 are all divisible either by 7 or by 13

see picture below for calculation method and steps leading to given result. 7 was chosen as starting number as any 2-digit number divisible by 7 or 13 is not ending with 7 (except 77 which can't be included)

red fonts indicate duplication of digits where caculation line ends