Solution: To find the number, compute the least common multiple (LCM) of 7 and 11, then add 1. Since 7 and 11 are coprime, $ extLCM(7, 11) = 7 imes 11 = 77$. Adding 1 gives $77 + 1 = 78$. The two-digit number is $oxed78$. - Groen Casting