This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
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# LCM

 LCMgives the least common multiple of the .
• Integer mathematical function, suitable for both symbolic and numerical manipulation.
• LCM works with ordinary and Gaussian integers.
• LCM works not only with integers but also with rational numbers, both real and complex.
• For rational numbers , LCM gives the least rational number r for which all the are integers.
• LCM automatically threads over lists.
Least common multiple of three integers:
Plot the LCM for a number with 1000:
Least common multiple of three integers:
 Out[1]=

Plot the LCM for a number with 1000:
 Out[1]=
 Scope   (4)
Use rational arguments:
Use with Gaussian integers:
 Applications   (6)
The LCM of the first integers:
Maximal order of group elements from the symmetric group of order (Landau's function):
Cumulative LCMs:
Plot the logarithm of the data (if Riemann's hypothesis holds, this grows linearly):
LCMs of Fibonacci numbers:
LCMs of binomial coefficients:
Compare with:
One-argument form:
Compute LCM from factorization:
Use in sums:
Simplify expressions containing LCM:
Reduce inequalities involving LCM:
LCM sorts its arguments: