common multiple
Noun
Meaning
an integer that is a multiple of two or more other integers
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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.
Footnote 27, p. 9: "For example, the natural numbers with gcd (greatest common divisor) as meet and lcm (least common multiple) as join operation determine a (complete distributive) lattice."
Given two positive integers their least common multiple and greatest common divisor are given by the formulas : and : Since : this gives : In fact, any rational number can be written uniquely as the product of primes if negative exponents are allowed.
Notation In this article we will denote the least common multiple of two integers a and b as lcm(a, b).