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LCM




Mathematica Notation

Traditional Notation









Integer Functions > LCM[n1,n2,...,nm] > Specific values > Specialized values





http://functions.wolfram.com/04.10.03.0007.01









  


  








Input Form





LCM[GCD[n, p], GCD[n, q]] == GCD[n, LCM[p, q]] /; Element[n, Integers] && n > 0 && Element[p, Integers] && p > 0 && Element[q, Integers] && q > 0








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["LCM", "[", RowBox[List[RowBox[List["GCD", "[", RowBox[List["n", ",", "p"]], "]"]], ",", RowBox[List["GCD", "[", RowBox[List["n", ",", "q"]], "]"]]]], "]"]], "\[Equal]", RowBox[List["GCD", "[", RowBox[List["n", ",", RowBox[List["LCM", "[", RowBox[List["p", ",", "q"]], "]"]]]], "]"]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", ">", "0"]], "\[And]", RowBox[List["p", "\[Element]", "Integers"]], "\[And]", RowBox[List["p", ">", "0"]], "\[And]", RowBox[List["q", "\[Element]", "Integers"]], "\[And]", RowBox[List["q", ">", "0"]]]]]]]]








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> lcm </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mi> gcd </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> n </mi> <mo> , </mo> <mi> p </mi> </mrow> <mo> ) </mo> </mrow> <mo> , </mo> <mrow> <mi> gcd </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> n </mi> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mi> gcd </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> n </mi> <mo> , </mo> <mrow> <mi> lcm </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> p </mi> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> n </mi> <mo> &#8712; </mo> <msup> <mi> &#8469; </mi> <mo> + </mo> </msup> </mrow> <mo> &#8743; </mo> <mrow> <mi> p </mi> <mo> &#8712; </mo> <msup> <mi> &#8469; </mi> <mo> + </mo> </msup> </mrow> <mo> &#8743; </mo> <mrow> <mi> q </mi> <mo> &#8712; </mo> <msup> <mi> &#8469; </mi> <mo> + </mo> </msup> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <lcm /> <apply> <gcd /> <ci> n </ci> <ci> p </ci> </apply> <apply> <gcd /> <ci> n </ci> <ci> q </ci> </apply> </apply> <apply> <gcd /> <ci> n </ci> <apply> <lcm /> <ci> p </ci> <ci> q </ci> </apply> </apply> </apply> <apply> <and /> <apply> <in /> <ci> n </ci> <apply> <ci> SuperPlus </ci> <ci> &#8469; </ci> </apply> </apply> <apply> <in /> <ci> p </ci> <apply> <ci> SuperPlus </ci> <ci> &#8469; </ci> </apply> </apply> <apply> <in /> <ci> q </ci> <apply> <ci> SuperPlus </ci> <ci> &#8469; </ci> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LCM", "[", RowBox[List[RowBox[List["GCD", "[", RowBox[List["n_", ",", "p_"]], "]"]], ",", RowBox[List["GCD", "[", RowBox[List["n_", ",", "q_"]], "]"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["GCD", "[", RowBox[List["n", ",", RowBox[List["LCM", "[", RowBox[List["p", ",", "q"]], "]"]]]], "]"]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", ">", "0"]], "&&", RowBox[List["p", "\[Element]", "Integers"]], "&&", RowBox[List["p", ">", "0"]], "&&", RowBox[List["q", "\[Element]", "Integers"]], "&&", RowBox[List["q", ">", "0"]]]]]]]]]]


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





2001-10-29