The change in number densities of aqueous solutions of alkali chlorides should be qualitatively predictable. Typically, as cations get bigger the number density of the solution decreases. However, aqueous solutions of lithium and sodium chloride exhibit at ambient conditions practically identical number densities at equal molalities despite different ionic sizes. Here, we provide an atomistic interpretation of this experimentally observed anomalous behavior using molecular dynamics simulations. The obtained results show that rigidity of the Li+ first and second solvation shells and associated compromised hydrogen bonding result in practically equal average water densities in the local hydration regions for Li+ and Na+ despite different sizes of the cations. In addition, in more distant regions from the cations, the water densities of these two solutions also coincide. These findings thus provide an atomistic interpretation for matching number densities of LiCl and NaCl solutions. In contrast, the number density differences between NaCl and KCl solutions, as well as between LiCl and KCl solutions behave in a regular fashion with lower number densities of solutions observed for larger cations.