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LCM




Mathematica Notation

Traditional Notation









Integer Functions > LCM[n1,n2,...,nm] > Representations through equivalent functions > With related functions





http://functions.wolfram.com/04.10.27.0005.01









  


  








Input Form





GCD[LCM[k, m], LCM[k, n], LCM[m, n]] == LCM[GCD[k, m], GCD[k, n], GCD[m, n]] /; Element[{n, m, k}, Integers]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["GCD", "[", RowBox[List[RowBox[List["LCM", "[", RowBox[List["k", ",", "m"]], "]"]], ",", RowBox[List["LCM", "[", RowBox[List["k", ",", "n"]], "]"]], ",", RowBox[List["LCM", "[", RowBox[List["m", ",", "n"]], "]"]]]], "]"]], "\[Equal]", RowBox[List["LCM", "[", RowBox[List[RowBox[List["GCD", "[", RowBox[List["k", ",", "m"]], "]"]], ",", RowBox[List["GCD", "[", RowBox[List["k", ",", "n"]], "]"]], ",", RowBox[List["GCD", "[", RowBox[List["m", ",", "n"]], "]"]]]], "]"]]]], "/;", RowBox[List["Element", "[", RowBox[List[RowBox[List["{", RowBox[List["n", ",", "m", ",", "k"]], "}"]], ",", "Integers"]], "]"]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mi> gcd </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mi> lcm </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> k </mi> <mo> , </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> , </mo> <mrow> <mi> lcm </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> k </mi> <mo> , </mo> <mi> n </mi> </mrow> <mo> ) </mo> </mrow> <mo> , </mo> <mrow> <mi> lcm </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> m </mi> <mo> , </mo> <mi> n </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mi> lcm </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mi> gcd </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> k </mi> <mo> , </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> , </mo> <mrow> <mi> gcd </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> k </mi> <mo> , </mo> <mi> n </mi> </mrow> <mo> ) </mo> </mrow> <mo> , </mo> <mrow> <mi> gcd </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> m </mi> <mo> , </mo> <mi> n </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mo> { </mo> <mrow> <mi> n </mi> <mo> , </mo> <mi> m </mi> <mo> , </mo> <mi> k </mi> </mrow> <mo> } </mo> </mrow> <mo> &#8712; </mo> <semantics> <mi> &#8484; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalZ]&quot;, Function[Integers]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <gcd /> <apply> <lcm /> <ci> k </ci> <ci> m </ci> </apply> <apply> <lcm /> <ci> k </ci> <ci> n </ci> </apply> <apply> <lcm /> <ci> m </ci> <ci> n </ci> </apply> </apply> <apply> <lcm /> <apply> <gcd /> <ci> k </ci> <ci> m </ci> </apply> <apply> <gcd /> <ci> k </ci> <ci> n </ci> </apply> <apply> <gcd /> <ci> m </ci> <ci> n </ci> </apply> </apply> </apply> <apply> <in /> <list> <ci> n </ci> <ci> m </ci> <ci> k </ci> </list> <integers /> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["GCD", "[", RowBox[List[RowBox[List["LCM", "[", RowBox[List["k_", ",", "m_"]], "]"]], ",", RowBox[List["LCM", "[", RowBox[List["k_", ",", "n_"]], "]"]], ",", RowBox[List["LCM", "[", RowBox[List["m_", ",", "n_"]], "]"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["LCM", "[", RowBox[List[RowBox[List["GCD", "[", RowBox[List["k", ",", "m"]], "]"]], ",", RowBox[List["GCD", "[", RowBox[List["k", ",", "n"]], "]"]], ",", RowBox[List["GCD", "[", RowBox[List["m", ",", "n"]], "]"]]]], "]"]], "/;", RowBox[List[RowBox[List["{", RowBox[List["n", ",", "m", ",", "k"]], "}"]], "\[Element]", "Integers"]]]]]]]]


Date Added to functions.wolfram.com (modification date)





2001-10-29