Proposition: 7.22: Numbers forming Fraction in Lowest Terms are Coprime
(Proposition 22 from Book 7 of Euclid's “Elements”)
The least numbers of those (numbers) having the same ratio as they are prime to one another.
Modern Formulation
This is the converse of Prop 7.21. If two natural numbers form a fraction $\frac AB$ and they are the smallest numbers forming this fraction, then they are coprime.
Table of Contents
Proofs: 1
Mentioned in:
Proofs: 1 2 3 4
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References
Adapted from (subject to copyright, with kind permission)
 Fitzpatrick, Richard: Euclid's "Elements of Geometry"
Adapted from CC BYSA 3.0 Sources:
 Prime.mover and others: "Pr∞fWiki", https://proofwiki.org/wiki/Main_Page, 2016