We present high-resolution archival Atacama Large Millimeter/submillimeter Array (ALMA) CO J=3-2 and J=6-5 and HCO+ J=4-3 observations and new CARMA CO and 13CO J=1-0 observations of the luminous infrared galaxy NGC 1614. The high-resolution maps show the previously identified ring-like structure while the CO J=3-2 map shows extended emission that traces the extended dusty features. We combined these new observations with previously published Submillimeter Array CO and 13CO J=2-1 observations to constrain the physical conditions of the molecular gas at a resolution of 230 pc using a radiative transfer code and a Bayesian likelihood analysis. At several positions around the central ring-like structure, the molecular gas is cold (20-40 K) and dense (> 10^{3.0} cm^{-3}) . The only region that shows evidence of a second molecular gas component is the hole in the ring. The CO-to-13CO abundance ratio is found to be greater than 130, more than twice the local interstellar medium value. We also measure the CO-to-H_{2} conversion factor, alpha_{CO}, to range from 0.9 to 1.5 M_sol (K km/s pc^{2})^{-1}.
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