First, check if perhaps there are no solutions because a divisor of \(51\) and \(87\) is not a divisor of \(123\text{.}\) Really, we just need to check whether \(\gcd(51, 87) \mid 123\text{.}\) This greatest common divisor is 3, and yes \(3 \mid 123\text{.}\) At this point, we might as well factor out this greatest common divisor. So instead, we will solve: