Proposition: 7.35: Least Common Multiple Divides Common Multiple
(Proposition 35 from Book 7 of Euclid's “Elements”)
If two numbers (both) measure some number then the least (number) measured by them will also measure the same (number).
* For let two numbers, $A$ and $B$, (both) measure some number $CD$, and (let) $E$ (be the) least (number measured by both $A$ and $B$).
* I say that $E$ also measures $CD$.
see least common multiple.
Table of Contents
Proofs: 1 2
Adapted from (subject to copyright, with kind permission)
- Fitzpatrick, Richard: Euclid's "Elements of Geometry"
Adapted from CC BY-SA 3.0 Sources:
- Prime.mover and others: "Pr∞fWiki", https://proofwiki.org/wiki/Main_Page, 2016