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For example, 10 is a multiple of 5 because 5 × 2 = 10, so 10 is divisible by 5 and 2. Because 10 is the smallest positive integer that is divisible by both 5 and 2, it is the least common multiple of 5 and 2. By the same principle, 10 is the least common multiple of −5 and −2 as well.
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.
Here, 36 is the least common multiple of 12 and 18. Their product, 216, is also a common denominator, but calculating with that denominator involves larger numbers:
LCM may refer to: Computing and mathematics. Latent class model, a concept in statistics; Least common multiple, a function of two integers; Living Computer Museum;
It is the least common multiple of the numbers from 1 to 8. [4] It is the smallest number divisible by every natural number from 1 to 10, except 9. It is the largest number k such that all coprime quadratic residues modulo k are squares. In this case, they are 1, 121, 169, 289, 361 and 529. [5] It is an evil number.
210 is an abundant number, [1] and Harshad number. It is the product of the first four prime numbers (2, 3, 5, and 7), and thus a primorial, [2] where it is the least common multiple of these four prime numbers. 210 is the first primorial number greater than 2 which is not adjacent to 2 primes (211 is prime, but 209 is not).
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:
The least common multiple of numbers from 1 through 7; [4] as a consequence of that, it is a Harshad number in bases 2 to 10, except in base 5. a 141-gonal number. [citation needed] a balanced number. [5] largely composite number [6]