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LCM

LCM
gives 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:
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Click for copyable input
Out[1]=
 
Plot the LCM for a number with 1000:
In[1]:=
Click for copyable input
Out[1]=
LCM threads element-wise over lists:
Use rational arguments:
Use with Gaussian integers:
TraditionalForm formatting:
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:
Signs are discarded:
The arguments must be explicit integers:
Plot the argument of the Fourier transform of the LCMs:
Form LCMs of 1 with rational numbers:
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