So we need a number x such that 55+x and 45 have 9 as gcd. The multiples of 9 are
[tex]\begin{gathered} 9, \\ 18, \\ 27, \\ 36, \\ 45, \\ 54, \\ 63, \\ \ldots \end{gathered}[/tex]Then, the next multiple of 9 after 55 is 63, so if we add x=8 to 55, then
[tex]\begin{gathered} 63=7\times9 \\ 45=5\times9 \end{gathered}[/tex]63 and 45 have 9 as their gcd. Then the answer is x=8.
