Least common multiple

English

Noun

1. Template:Lb The smallest positive integer which is divisible by (equivalently, is an integer multiple of) each of a specified finite set of integers.

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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 $\mathrm{LCM}(a,b),\mathrm{lcm}(a,b),\mathrm{l.c.m.}(a,b)$ and $[a,b]$.

Synonyms

• Template:Sense Template:L, Template:L, Template:L Template:Qualifier

Coordinate terms

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Related terms

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Translations

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References

• 2008, Template:W, Template:W (6th ed. editors), Template:W, Template:W, An Introduction to the Theory of Numbers, 6th Edition Template:W, Paperback, page 57.

Further reading

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• Least common multiple on Template:W
• Least Common Multiple on Template:W