Built-in Mathematica Symbol

LCM

LCM[n₁, n₂, ...]
gives the least common multiple of the n_i.

Integer mathematical function, suitable for both symbolic and numerical manipulation.

LCM works not only with integers but also with rational numbers, both real and complex.

For rational numbers r_i, LCM[r₁, r₂, ...] gives the least rational number r for which all the r/r_i are integers.

Least common multiple of three integers:

Plot the LCM for a number with 1000:

Least common multiple of three integers:

Plot the LCM for a number with 1000:

LCM threads element-wise over lists:

Use rational arguments:

Use with Gaussian integers:

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: