In this work the Lennard Jones (12-6) potential and the Lorentz-Bertholet combining rules have been used to calculate the linear isotherm regularity (LIR) parameters for a hypothetical pure fluid in which all the molecular interactions are unlike one another. It can be shown that whenever the sizes and potential well depths are the same for the two components, these parameters are obtained from the "mean geometric approximation" or simply "MGA". The values of these parameters have been used to calculate the density of binary and ternary mixtures, for mixtures of inert gases, nonpolar, polar, and strongly hydrogen-bonded systems, at different temperatures, pressures, and mole fractions. The calculated results show a maximum deviation less than 1.6%, except for the strongly hydrogen-bonded system of CH3OH/H2O for which the maximum deviation is 2.4%. For the cases in which there is a remarkable difference between molecular sizes and/or the potential well depths of the components, or when a more accurate result is needed, the parameters have been calculated by using an equation more accurate than the MGA. However, the results reveal that the MGA is an excellent approximation for all systems including atomic-atomic, polar-nonpolar, hydrocarbons, and strongly hydrogen-bonded mixtures. Even in the cases where the value of the molecular sizes and/or the potential well depths are quite different, the deviation given by MGA is small. By use of the temperature dependence of LIR parameters, the density has also been calculated at temperatures other than that of the pure components. In this case the calculated values are in excellent agreement with the experimental values.