Which is the correct comparative or superlative adverb?

Question

Of all Kate's fans, her family cheers more loudly or most loudly at games.

When comparing her with one other person (so that two people are being compared), use the -er word or the word "more" with the adjective or adverb.

When comparing her with two or more other people (so that three or more people are being compared), use the -est word or the word "most" with the adjective or adverb.

http://grammar.ccc.commnet.edu/grammar/adjectives.htm
Scroll down to Degrees of Adjectives.

http://www.lousywriter.com/adjectives_comparison.php

http://www.uottawa.ca/academic/arts/writcent/hypergrammar/compsupl.html

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