N49 (LHA 120-N49) is a bright X-ray supernova remnant (SNR) in the Large Magellanic Cloud. We present new $^{12}$CO($J$ = 1-0, 3-2), HI, and 1.4 GHz radio-continuum observations of the SNR N49 using Mopra, ASTE, ALMA, and ATCA. We have newly identified three HI clouds using ATCA with an angular resolution of ~20: one associated with the SNR and the others located in front of the SNR. Both the CO and HI clouds in the velocity range from 280-291 km s$^{-1}$ are spatially correlated with both the soft X-rays (0.2-1.2 keV) and the hard X-rays (2.0-7.0 keV) of N49 on a ~10 pc scale. CO 3-2/1-0 intensity ratios indicate higher values of the CO cloud toward the SNR shell with an angular resolution of ~45, and thus a strong interaction was suggested. Using the ALMA, we have spatially resolved CO clumps embedded within or along the southeastern rim of N49 with an angular resolution of ~3. Three of the CO clumps are rim-brightened on a 0.7-2 pc scale in both hard X-rays and the radio continuum$:$ this provides further evidence for dynamical interactions between the CO clumps and the SNR shock wave. The enhancement of the radio synchrotron radiation can be understood in terms of magnetic-field amplification around the CO clumps via a shock-cloud interaction. We also present a possible scenario in which the recombining plasma that dominates the hard X-rays from N49 was formed via thermal conduction between the SNR shock waves and the cold$/$dense molecular clumps.
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