gives the least common multiple of the ni.
- LCM is also known as smallest common multiple.
- Integer mathematical function, suitable for both symbolic and numerical manipulation.
- LCM[n1,n2,…] is the smallest positive integer that is a multiple of each of the integers n1,n2,….
- For rational numbers ri, LCM[r1,r2,…] gives the least rational number r for which all the r/ri are integers.
- LCM works over Gaussian integers.
Examplesopen allclose all
Basic Examples (2)
Numerical Manipulation (7)
Symbolic Manipulation (4)
Basic Applications (4)
Number Theory (5)
Maximal order of group elements from the symmetric group of order n (Landau's function):
LCMs of binomial coefficients:
Simplify expressions containing LCM:
Properties & Relations (7)
The LCM of coprime numbers is equal to their product:
LCM for prime numbers is their product:
LCM for prime power representation :
LCM is commutative :
LCM is associative :
LCM is distributive :
Possible Issues (3)
LCM sorts its arguments:
Wolfram Research (1988), LCM, Wolfram Language function, https://reference.wolfram.com/language/ref/LCM.html (updated 1999).
Wolfram Language. 1988. "LCM." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 1999. https://reference.wolfram.com/language/ref/LCM.html.
Wolfram Language. (1988). LCM. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/LCM.html