Future weak lensing surveys potentially hold the highest statistical power for constraining cosmological parameters compared to other cosmological probes. The statistical power of a weak lensing survey is determined by the sky coverage, the inverse of the noise in shear measurements, and the galaxy number density. The combination of the latter two factors is often expressed in terms of $n_{rm eff}$ -- the effective number density of galaxies used for weak lensing measurements. In this work, we estimate $n_{rm eff}$ for the Large Synoptic Survey Telescope (LSST) project, the most powerful ground-based lensing survey planned for the next two decades. We investigate how the following factors affect the resulting $n_{rm eff}$ of the survey with detailed simulations: (1) survey time, (2) shear measurement algorithm, (3) algorithm for combining multiple exposures, (4) inclusion of data from multiple filter bands, (5) redshift distribution of the galaxies, and (6) masking and blending. For the first time, we quantify in a general weak lensing analysis pipeline the sensitivity of $n_{rm eff}$ to the above factors. We find that with current weak lensing algorithms, expected distributions of observing parameters, and all lensing data ($r$- and $i$-band, covering 18,000 degree$^{2}$ of sky) for LSST, $n_{rm eff} approx37$ arcmin$^{-2}$ before considering blending and masking, $n_{rm eff} approx31$ arcmin$^{-2}$ when rejecting seriously blended galaxies and $n_{rm eff} approx26$ arcmin$^{-2}$ when considering an additional 15% loss of galaxies due to masking. With future improvements in weak lensing algorithms, these values could be expected to increase by up to 20%. Throughout the paper, we also stress the ways in which $n_{rm eff}$ depends on our ability to understand and control systematic effects in the measurements.
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