  We present IRAM-30m Telescope $^{12}$CO and $^{13}$CO observations of a
sample of 55 luminous and ultraluminous infrared galaxies (LIRGs and ULIRGs) in
the local universe. This sample is a subset of the Great Observatory All-Sky
LIRG Survey (GOALS), for which we use ancillary multi-wavelength data to better
understand their interstellar medium and star formation properties. Fifty-three
(96%) of the galaxies are detected in $^{12}$CO, and 29 (52%) are also detected
in $^{13}$CO above a 3$\sigma$ level. The median full width at zero intensity
(FWZI) velocity of the CO line emission is 661km s$^{-1}$, and $\sim$54% of the
galaxies show a multi-peak CO profile. Herschel photometric data is used to
construct the far-IR spectral energy distribution of each galaxy, which are fit
with a modified blackbody model that allows us to derive dust temperatures and
masses, and infrared luminosities. We make the assumption that the gas-to-dust
mass ratio of (U)LIRGs is comparable to local spiral galaxies with a similar
stellar mass (i.e., gas/dust of mergers is comparable to their progenitors) to
derive a CO-to-H$_2$ conversion factor of
$\langle\alpha\rangle=1.8^{+1.3}_{-0.8}M_\odot$(K km s$^{-1}$pc$^{2}$)$^{-1}$;
such a value is comparable to that derived for (U)LIRGs based on dynamical mass
arguments. We derive gas depletion times of $400-600$Myr for the (U)LIRGs,
compared to the 1.3Gyr for local spiral galaxies. Finally, we re-examine the
relationship between the $^{12}$CO/$^{13}$CO ratio and dust temperature,
confirming a transition to elevated ratios in warmer systems.
