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A multiple of a number is the product of that number and an integer. 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.
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;
Order HCN n prime factorization prime exponents number of prime factors d(n) primorial factorization 1 1: 0 1 2 2* : 1 1 2 3 4: 2 2 3 4 6* : 1,1 2 4 5 12* : 2,1 3 6 6 24
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.
A 24-by-60 rectangle is covered with ten 12-by-12 square tiles, where 12 is the GCD of 24 and 60. More generally, an a-by-b rectangle can be covered with square tiles of side length c only if c is a common divisor of a and b.
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For example, the integers 6, 10, 15 are coprime because 1 is the only positive integer that divides all of them. If every pair in a set of integers is coprime, then the set is said to be pairwise coprime (or pairwise relatively prime, mutually coprime or mutually relatively prime). Pairwise coprimality is a stronger condition than setwise ...