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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.
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
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.
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.
A logarithmic chart allows only positive values to be plotted. A square root scale chart cannot show negative values. x: the x-values as a comma-separated list, for dates and time see remark in xType and yType; y or y1, y2, …: the y-values for one or several data series, respectively. For pie charts y2 denotes the radius of the corresponding ...
d() is the number of positive divisors of n, including 1 and n itself; σ() is the sum of the positive divisors of n, including 1 and n itselfs() is the sum of the proper divisors of n, including 1 but not n itself; that is, s(n) = σ(n) − n
Note: The American records should not be confused with the Americas records, which are the fastest times ever swum by a swimmer representing any country of the Americas. An asterisk (*) indicates that this record has been achieved since the latest USA Swimming records publication. A plus (+) indicates that this record also is the current world ...