Wiki source code of lcm

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1 h1. Least Common Multiple Notations
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3 In arithmetic and number theory, The least common multiple of two numbers {html}\\(a\\){html} and {html}\\(b\\){html}, variously denoted {html}\\(LCM(a,b)\\){html}.
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5 h3. Semantic
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7 - OpenMath's [arith1/lcm|http://www.openmath.org/cd/arith1.xhtml#lcm]
8 - lcm in [mathML|http://www.w3.org/TR/MathML3/chapter4.html#contm.lcm]
9 - lcm in [mathWorld|http://mathworld.wolfram.com/LeastCommonMultiple.html]
10 - lcm in [wikipedia|http://en.wikipedia.org/wiki/Least_common_multiple]
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13 h2. Observations of LCM
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17 h4. Dutch (Belgium)
18 The notation on the right (for _kleinste gemeen veelvoud_) is found in [Relaties en Structuren|Census.Bibliography#relens-frankdeclerck] (page 48).
19 [Download and preview the book|http://staff.science.uva.nl/~craats/BasisboekWiskunde2HP.pdf page 21].
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21 !lcm-du-lc.png|align=right!
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25 h4. Arabic (Saudi Arabia)
26 In Saudi Arabia and some other provinces we find the high-school math book represents the least common multiple in Arabic context. the example shows _LCM_ for 8 and 9, _م.م.أ_ means _LCM_. [Go to the example at the end of page 79 in the high school math book from ministry of education in Saudi Arabia|http://wiki.math-bridge.org/download/attachments/2883871/mathHighSchool1_part+1.pdf] or find [the math book for grade VII in our bibliography|Census.Bibliography#arMath-gradeVII]
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28 !lcm1-ar.png|align=right!
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32 h4. English
33 We find in [the discrete math|Census.Bibliography#discrete-math-GriesAndShneider] book the example represents the least common multiple in English context.
34 [Go direcly to page 317|http://books.google.com/books?id=ZWTDQ6H6gsUC&lpg=PA201&dq=superset%20math&pg=PA317#v=onepage&q=&f=false].
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36 !lcm1-en.png|align=right!
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40 h4. German
41 The example on the right denotes the least common multiple in the German book [Lineare Algebra|Census.Bibliography#lineareAlgebra-KowalskyMichler], and it is called 'Kleinstes gemeinsames Vielfaches' in german context.
42 [Go to the example in page 307|http://books.google.com/books?id=Lqn-1XzurJ4C&lpg=PA307&dq=Gr%C3%B6%C3%9Fter%20gemeinsamer%20Teiler&pg=PA307#v=onepage&q=&f=false].
43 Also you can find the same example in the German book [Zahlentheorie und Arithmetik, p. 125|Census.Bibliography#ZahlentheorieundArithmetik-Padberg]
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45 !lcm1-de.png|align=right!
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49 h4. Spanish
50 The Spanish [website for mathematics|http://matematicasies.com/?Calcular-el-minimo-comun-multiplo,717] shows the least common multiple in Spanish context.
51 We also find [wikipedia|http://es.wikipedia.org/wiki/M%C3%ADnimo_com%C3%BAn_m%C3%BAltiplo] shows another example in Spanish.
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53 !lcm1-sp.png|align=right! !lcm2-sp.png|align=right!
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57 h4. French
58 The example in page 173 represents the least common multiple in French context. [find the example|http://books.google.com/books?id=-ICoxQEGWT4C&lpg=PA172&dq=petit%20commun%20multiple&lr=&pg=PA173#v=onepage&q=&f=false] or find the book in [bibliography|Census.Bibliography#MathematiquesDiscretes-Hans-Heinrich].
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60 !lcm1-fr.png|align=right!
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64 h4. Finnish
65 We find that on the Helsinki University of Technology, [Department of Mathematics website|https://matta.hut.fi/matta2/isom/html/alkutekj3.html] they use _pyj_ instead of lcm, and it is called 'Pienin yhteinen jaettava' in Finnish context.
66 Also find the same ' _pyj_ ' example in [wikipedia|http://fi.wikipedia.org/wiki/Pienin_yhteinen_jaettava]. Another notation for lcm is _pym_ (pienin yhteinen monikerta). For example, this notation is used in University of Tampere, [Lecture notes by Pentti Haukkanen|http://mtl.uta.fi/Opetus/Algebra/algI04.pdf]. Usually at university level notation \[_a,b_\] is used for least common multiple of numbers _a_ and _b_ instead of letter combinations _pym_ or _pyj_. This notation is also used in lecture notes mentioned before.
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68 !pyg1-fi.png|align=right! \\ \\ \\
69 !pym.png|align=right!
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73 h3. Encoding LCM observations
74 [See encodings|http://devdemo.activemath.org/mathbridge/tools/symbolpresentation.cmd?order=by+Theory&lang=x-all&fmt=html&clipCoordinate=2&noApplet=true&omsource=%3COMOBJ+xmlns%3D%22http%3A%2F%2Fwww.openmath.org%2FOpenMath%22%3E%0D%0A++%3COMA%3E%0D%0A++++%3COMS+name%3D%22lcm%22+cd%3D%22arith1%22+xref%3D%22mbase%3A%2F%2Fopenmath-cds%2Farith1%2Flcm%22+%2F%3E%0D%0A++++%3COMV+name%3D%22a%22+%2F%3E%0D%0A++++%3COMV+name%3D%22b%22+%2F%3E%0D%0A++%3C%2FOMA%3E%0D%0A%3C%2FOMOBJ%3E&submit=View]
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