X\(^{a+}\) and Y\(^{b+}\) are hydrogen-like species. The wavelength of light absorbed during the transition between the states with principal quantum numbers \(n = 1\) and \(n = 2\) of X\(^{a+}\) is \(\lambda\). The wavelength of light absorbed during the transition between the states with principal quantum numbers \(n = 2\) and \(n = 4\) of Y\(^{b+}\) is \(9\lambda\). The lowest possible value of \((a+b)\) is _______.