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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.
Synonyms for GCD include greatest common factor (GCF), highest common factor (HCF), highest common divisor (HCD), and greatest common measure (GCM). The greatest common divisor is often written as gcd( a , b ) or, more simply, as ( a , b ) , [ 3 ] although the latter notation is ambiguous, also used for concepts such as an ideal in the ring of ...
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:
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;
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The least common multiple of a and b is equal to their product ab, i.e. lcm(a, b) = ab. [4] As a consequence of the third point, if a and b are coprime and br ≡ bs (mod a), then r ≡ s (mod a). [5] That is, we may "divide by b" when working modulo a.