least common multiple

== English == === Pronunciation === === Noun === least common multiple (plural least common multiples) (number theory) The smallest positive integer which is divisible by (equivalently, is an integer multiple of) each of a specified finite set of integers. ==== Usage notes ==== The requirement that the least common multiple be positive has two effects: It excludes zero, which is trivially divisible by any integer. It means that the specified set cannot contain an element equal to zero. (This is also achieved by the requirement that the numbers be divisors, zero not being a valid divisor of any number.) Notations used include LCM ⁡ ( a , b ) , lcm ⁡ ( a , b ) , l . c . m . ⁡ ( a , b ) {\displaystyle \operatorname {LCM} (a,b),\ \operatorname {lcm} (a,b),\ \operatorname {l.c.m.} (a,b)} and [ a , b ] {\displaystyle \ [a,b]} . ==== Synonyms ==== ((number theory)): lowest common multiple, smallest common multiple, lcm (initialism) ==== Coordinate terms ==== greatest common divisor ==== Related terms ==== least common denominator lowest common denominator ==== Translations ==== === References === 2008, D. R. Heath-Brown, J. H. Silverman (6th ed. editors), G. H. Hardy, E. M. Wright, An Introduction to the Theory of Numbers, 6th Edition Oxford University Press, Paperback, page 57. === Further reading === Greatest common divisor on Wikipedia.Wikipedia Least common multiple on Encyclopedia of Mathematics Least Common Multiple on Wolfram MathWorld