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 $B>A?$