
<A NAME=LCM>

<TITLE>LCM</TITLE></A>
<b><a href=r37_idx.html>INDEX</a></b><p><p>



<B>LCM</B> _ _ _  _ _ _  _ _ _  _ _ _ <B>switch</B><P>
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The <em>lcm</em> switch instructs REDUCE to compute the least common multiple 
of denominators whenever rational expressions occur. Default is <em>on</em>. 
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 <P> <H3> 
examples: </H3>
<P><PRE><TT>
off lcm; 

z := 1/(x**2 - y**2) + 1/(x-y)**2;  
			 


              2*X*(X - Y)
  Z := ------------------------- 
        4      3          3    4
       X  - 2*X *Y + 2*X*Y  - Y


on lcm; 

z; 

         2*X*(X - Y)
  ------------------------- 
   4      3          3    4
  X  - 2*X *Y + 2*X*Y  - Y


zz := 1/(x**2 - y**2) + 1/(x-y)**2;
			 


                 2*X
  ZZ := --------------------- 
         3    2        2    3
        X  - X *Y - X*Y  + Y


on gcd; 

z; 

           2*X
  ----------------------
   3    2        2    3
  X  - X *Y - X*Y  + Y

</TT></PRE><P>Note that <em>lcm</em> has effect only when rational expressions a
re first 
combined. It does not examine existing structures for simplifications on 
display. That is shown above when z is entered with 
<em>lcm</em> off. It remains unsimplified even after <em>lcm</em> is turned 
back on. However, a new variable containing the same expression is 
simplified on entry. The switch 
<A HREF=r37_0086.html>gcd</A> does examine existing 
structures, as shown in the last example line above. 
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Full greatest common divisor calculations become expensive if work with 
large rational expressions is required. A considerable savings of time 
can be had if a full gcd check is made only when denominators are combined, 
and only a partial check for numerators. This is the effect of the <em>lcm</em> 

switch. 
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