Chinese remainder theorem (CRT) provides an undersampling method to detect the frequency of a complex sinusoid. The detection of the multiple frequencies in a signal formed by the superposition of multiple complex sinusoids is a task frequently encountered in several applications such as phase unwrapping in radar signal processing and multiwavelength optical interferometry. A generalized CRT for multiple integers has recently been studied. In this letter, we complement it by giving two new conditions that ensure the maximal possible dynamic range for the multiple integers, i.e., the least common multiple (lcm) of all the moduli. Then, two corresponding determination algorithms are also proposed.