Most Common Multiple
R, 54 50 41 bytes



order(-tabulate(combn(scan(),2,prod)))[1]


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Alternatively, for 54 53 44 bytes:



names(sort(-table(combn(scan(),2,prod))))[1]


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In principle, the latter version outputs the relevant result even without the names function, but followed by the count of such most frequent products, which isn't asked for...

Thanks to CriminallyVulgar  for -4 and -1, and Giuseppe for -9 on both.