Least common multiple

The least common multiple of two or more integers is the smallest positive integer divisible by every integer in the set.

Prime factorization: The expression of an integer as a product of primes, unique up to the order of factors. Taking the highest exponent of each prime across the inputs constructs their least common multiple.
Common denominator: A denominator shared by two or more fractions. A least common multiple of denominators gives the smallest positive common denominator for fraction arithmetic.
Common multiple: An integer divisible by each of a given collection of integers. The least common multiple is the smallest positive member of the set of common multiples.
Integer: A whole number, its negative, or zero. The least common multiple is defined for collections of integers, with a positive result.
Greatest common divisor: The greatest positive integer that divides each of two or more integers. For positive integers, multiplying the inputs and dividing by their greatest common divisor gives their least common multiple.
Fraction addition: The operation of combining fractions into a sum, using a shared denominator when needed. The least common multiple can minimize the denominator used to add fractions.
Least common denominator: The smallest positive denominator divisible by all denominators in a collection of fractions. It is a fraction-specific use of the least common multiple.
Positive integer: An integer greater than zero. The positivity condition selects the least common multiple from positive shared multiples.
Euclidean algorithm: A repeated-division procedure for finding the greatest common divisor of two integers. It computes the greatest common divisor used in the efficient two-number least-common-multiple formula.
Periodic function: A function whose values repeat after a fixed positive interval called its period. Integer periods can share a least common multiple that marks a joint repetition interval.

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