  We present a systematic study of the low mass X-ray binary (LMXB) populations
of 6 elliptical galaxies. We utilize Chandra archival data to identify 665
X-ray point sources and HST archival data supplemented by ground observations
to identify 6173 GCs. We associate 209 LMXBs with red GC (RGC) and 76 LMXBs
with blue GCs (BGC), while we find no optical GC counterpart for 258 LMXBs.
This is the largest GC-LMXB sample studied so far. We confirm previous reports
suggesting that the fraction of GCs associated with LMXBs is 3 times larger in
RGCs than in BGCs, indicating that metallicity is a primary factor in the
GC-LMXB formation. While as already known, the brighter (and bigger) GCs have a
higher probability to host LMXBs, we find that this optical luminosity (or
mass) dependency is stronger in RGCs than in BGCs. We also find that GCs
located near the galaxy center have a higher probability to harbor LMXBs
compared to those in the outskirts. The radial distributions of GC-LMXBs (for
both RGC and BGC) are steeper than those of the whole optical GC sample, but
consistent with those of the optical halo light, suggesting that there must be
another parameter (in addition to metallicity) governing LMXB formation in GCs.
This second parameter must depend on the galacto-centric distance. We find no
statistically significant difference in the X-ray properties among RGC-LMXBs,
BGC-LMXBs and field-LMXBs. The similarity of the X-ray spectra of BGC-LMXBs and
RGC-LMXBs is inconsistent with the irradiation-induced stellar wind model
prediction. The similarity of the X-ray luminosity functions (XLFs) of GC-LMXBs
and field-LMXBs indicates that there is no significant difference in the
fraction of BH binaries present in these two populations, in contrast to
Galactic LMXBs where BH binaries are not found in GCs.
