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A least common multiple of a and b is a common multiple that is minimal, in the sense that for any other common multiple n of a and b, m divides n. In general, two elements in a commutative ring can have no least common multiple or more than one. However, any two least common multiples of the same pair of elements are associates. [10]
lcm(m, n) (least common multiple of m and n) is the product of all prime factors of m or n (with the largest multiplicity for m or n). gcd(m, n) × lcm(m, n) = m × n. Finding the prime factors is often harder than computing gcd and lcm using other algorithms which do not require known prime factorization.
In musical rhythm, the LCD is used in cross-rhythms and polymeters to determine the fewest notes necessary to count time given two or more metric divisions. For example, much African music is recorded in Western notation using 12 8 because each measure is divided by 4 and by 3, the LCD of which is 12.
Least common multiple, a function of two integers; Living Computer Museum; Life cycle management, management of software applications in virtual machines or in containers; Logical Computing Machine, another name for a Turing machine
Equivalently, g(n) is the largest least common multiple (lcm) of any partition of n, or the maximum number of times a permutation of n elements can be recursively applied to itself before it returns to its starting sequence. For instance, 5 = 2 + 3 and lcm(2,3) = 6. No other partition of 5 yields a bigger lcm, so g(5) = 6.
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SpringerProfessional information Lecture Notes in Computer Science is a series of computer science books published by Springer Science+Business Media since 1973. Overview
In statistics, a latent class model (LCM) is a model for clustering multivariate discrete data.It assumes that the data arise from a mixture of discrete distributions, within each of which the variables are independent.