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2. Least common multiple - Wikipedia

   en.wikipedia.org/wiki/Least_common_multiple

   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]

3. Greatest common divisor - Wikipedia

   en.wikipedia.org/wiki/Greatest_common_divisor

   gcd(a, b) is closely related to the least common multiple lcm(a, b): we have gcd(a, b)⋅lcm(a, b) = | a⋅b |. This formula is often used to compute least common multiples: one first computes the GCD with Euclid's algorithm and then divides the product of the given numbers by their GCD. The following versions of distributivity hold true:

4. Table of prime factors - Wikipedia

   en.wikipedia.org/wiki/Table_of_prime_factors

   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.

5. Euclidean algorithm - Wikipedia

   en.wikipedia.org/wiki/Euclidean_algorithm

   For example, 6 and 35 factor as 6 = 2 × 3 and 35 = 5 × 7, so they are not prime, but their prime factors are different, so 6 and 35 are coprime, with no common factors other than 1. A 24×60 rectangle is covered with ten 12×12 square tiles, where 12 is the GCD of 24 and 60.

6. Landau's function - Wikipedia

   en.wikipedia.org/wiki/Landau's_function

   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.

7. Polynomial greatest common divisor - Wikipedia

   en.wikipedia.org/wiki/Polynomial_greatest_common...

   x 2 − 5x − 6 = (12 x + 12) (⁠ 1 / 12 ⁠ x − ⁠ 1 / 2 ⁠) + 0 Since 12 x + 12 is the last nonzero remainder, it is a GCD of the original polynomials, and the monic GCD is x + 1 . In this example, it is not difficult to avoid introducing denominators by factoring out 12 before the second step.

8. Lowest common denominator - Wikipedia

   en.wikipedia.org/wiki/Lowest_common_denominator

   Download as PDF; Printable version; ... 36 is the least common multiple of 12 and 18. Their product, 216, is also a common denominator, but calculating with that ...

9. Fraction - Wikipedia

   en.wikipedia.org/wiki/Fraction

   6 1 2 1 1 −1 4 5 9. and would be written in modern notation as 6 ⁠ 1 / 4 ⁠, 1 ⁠ 1 / 5 ⁠, and 2 − ⁠ 1 / 9 ⁠ (i.e., 1 ⁠ 8 / 9 ⁠). The horizontal fraction bar is first attested in the work of Al-Hassār (fl. 1200), [35] a Muslim mathematician from Fez, Morocco, who specialized in Islamic inheritance jurisprudence.