We report the results of a sensitive search for 12.2 GHz methanol maser emission towards a sample of eight high-mass star formation regions in the Large Magellanic Clouds which have been detected in other maser transitions. We detected one source towards the star formation region N105a. This is the first detection of a 12.2 GHz methanol maser outside our Galaxy. We also made near-contemporaneous observations of the 6.7 GHz methanol and 22 GHz water masers towards these sources, resulting in the detection of water maser emission in six new sources, including one associated with the strongest 6.7 GHz maser in the Magellanic Clouds IRAS 05011-6815. The majority of the maser sources are closely associated with objects identified as likely Young Stellar Objects (YSO) on the basis of Spitzer Space Telescope observations. We find that the YSOs associated with masers tend to be more luminous and have redder infrared colours than the sample as a whole. SED modeling of the YSOs shows that the masers are associated with sources of higher central mass, total luminosity and ambient density than the majority of YSOs in the LMC. This is consistent with the well-established relationship between luminous methanol and water masers and young, high-mass objects observed in the Galaxy.
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