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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]
In the common case where m is a power of 2 and a ≡ 5 (mod 8) (a desirable property for other reasons), it is always possible to find an initial value X 0 so that the denominator X 1 − X 0 ≡ ±1 (mod m), producing an even simpler relationship.
[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.
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The generator polynomial of the BCH code is defined as the least common multiple g(x) = lcm(m 1 (x),…,m d − 1 (x)). It can be seen that g(x) is a polynomial with coefficients in GF(q) and divides x n − 1. Therefore, the polynomial code defined by g(x) is a cyclic code.
Gaṇitasārasan̄graha (Compendium on the gist of Mathematics) is a mathematics text written by Māhāvīrācharya.It is first text completely written on mathematics with questions asked in it being completely different from one asked in previous texts composed in Indian subcontinent.
Download QR code; Print/export Download as PDF; Printable version; In other projects ... Here, 36 is the least common multiple of 12 and 18. Their product, 216, is ...
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.