  Context: We investigated the molecular gas associated with 6.7 GHz methanol
masers throughout the Galaxy using a J=1-0 transition of the CO isotopologues.
  Methods:Using the 13.7-meter telescope at the Purple Mountain Observatory
(PMO), we have obtained ^{12}CO and ^{13}CO (1-0) lines for 160 methanol masers
sources from the first to the third Galactic quadrants. We made efforts to
resolve the distance ambiguity by careful comparison with the radio continuum
and HI 21 cm observations.
  Results: First, the maser sources show increased ^{13}CO line widths toward
the Galactic center, suggesting that the molecular gas are more turbulent
toward the Galactic center. This trend can be noticeably traced by the ^{13}CO
line width. Second, the ^{12}CO excitation temperature shows a noticeable
correlation with the H_2 column density. A possible explanation consistent with
the collapse model is that the higher surface-density gas is more efficient to
the stellar heating and/or has a higher formation rate of high-mass stars.
Third, comparing the IRDCs, the maser sources on average have significantly
lower H_2 column densities, moderately higher temperatures, and similar line
widths. Fourth, in the mapped regions, 51 ^{13}CO cores have been revealed.
Only 17 coincide with the radio continuum emission (F_{cm}>6 mJy), while a
larger fraction (30 cores) coincide with the infrared emissions. The IR-bright
and radio-bright sources exhibit significantly higher $^{12}$CO excitation
temperatures than the IR-faint and radio-faint sources, respectively.
  Conclusions: The 6.7 GHz masers show a moderately low ionization rate but
have a common-existing stellar heating that generates the IR emissions. The
relevant properties can be characterized by the ^{12}CO and ^{13}CO (1-0)
emissions in several aspects as described above.
