Call the dividend is \(a\), the remainder is \(b\left(b\le10;b\in N\right)\)
So the quotient is \(b\)
Have: \(a=11\times b+b=12\times b\)
So \(a_{max}\Leftrightarrow12\times b_{max}\Leftrightarrow b_{max}\Leftrightarrow b=10\)
\(\Leftrightarrow a=12\times10=120\)
So the largest number is 120