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[14] and whose period is the least common multiple of the component periods. Although the periods will share a common divisor of 2, the moduli can be chosen so that is the only common divisor and the resultant period is (m 1 − 1)(m 2 − 1)···(m k − 1)/2 k−1. [2]: 744 One example of this is the Wichmann–Hill generator.
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]
The results of multiple LCG algorithms are combined through the CLCG algorithm to create pseudo-random numbers with a longer period than is achievable with the LCG method by itself. [ 3 ] The period of a CLCG is the least common multiple of the periods of the individual generators, which are one less than the moduli.
Tools. Tools. move to sidebar hide. Actions ... Download QR code; Print/export ... also known as the greatest common factor; Least common multiple;
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.
One method of producing a longer period is to sum the outputs of several LCGs of different periods having a large least common multiple; the Wichmann–Hill generator is an example of this form. (We would prefer them to be completely coprime, but a prime modulus implies an even period, so there must be a common factor of 2, at least.) This can ...
The arithmetic billiard for the numbers 15 and 40: the greatest common divisor is 5, the least common multiple is 120. In recreational mathematics, arithmetic billiards provide a geometrical method to determine the least common multiple and the greatest common divisor of two natural numbers by making use of reflections inside a rectangle whose sides are the two given numbers.
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