Extending the Definitions of GCD and LCM to Fractions

With the LCM and GCD of natural numbers well- defined and an integral part of the middle school curriculum, one may wonder why this article embarks on a rather theoretical study of the LCM and GCD of rational numbers. But this article depicts exactly what a mathematician does – take a well-known concept and extend it to larger sets, testing the extended definition with backward compatibility with the original set. For the more able middle-schooler, this is an excellent opportunity to flex the muscles of conceptual understanding and constructive reasoning. Dive in!

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