Divisible Sandwiches

Number Theory Level 2

Define \(A\) as follows: \[A=1\underbrace{0\cdots 0}_{n \text{ zeroes}}1,\] where \(n\) is a positive integer. Does there exist another number \(B\) similarly formed that is a multiple of \(A\): \[B=1\underbrace{0\cdots 0}_{m \text{ zeroes}}1\] such that \(B>A?\)