Math 2.0

Number theory Corollary

Lcm of coprime integers

Builds on Coprime integersLeast common multipleProduct of the gcd and the lcm

Statement

Let aa and bb be natural numbers that are coprime. Then lcm⁡(a,b)=ab\operatorname{lcm}(a, b) = a b.

Remarks

This follows from the product of the gcd and the lcm, because gcd⁡(a,b)=1\gcd(a, b) = 1. The converse is also true when aa and bb are positive: if lcm⁡(a,b)=ab\operatorname{lcm}(a, b) = a b, then aa and bb are coprime. For example, lcm⁡(8,15)=120\operatorname{lcm}(8, 15) = 120.

Reading path

To understand this page from the ground up, read these 6 pages in order. The foundations come first.

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Divisibility, definition, no evidence levelDivisibilitydefinitionGreatest common divisor, definition, no evidence levelGreatest common divis…definitionLeast common multiple, definition, no evidence levelLeast common multipledefinitionCoprime integers, definition, no evidence levelCoprime integersdefinitionProduct of the gcd and the lcm, statement, no evidence levelProduct of the gcd an…statementLcm of coprime integers, statement, no evidence levelLcm of coprime intege…statement
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Divisibility definition
  2. Greatest common divisor definition
  3. Least common multiple definition
  4. Coprime integers definition
  5. Product of the gcd and the lcm statement
  6. Lcm of coprime integers statement

Further reading

  1. Web https://en.wikipedia.org/wiki/Least_common_multiple, Using the greatest common divisor
About this page
Tag07CZYE06ZJ
URIm2://07CZYE06ZJ
Kindstatement, corollary
WritingW0 stub
MSC11A05
StatusThis copy of the site has no build data. Run m2 status 07CZYE06ZJ.
UsesCoprime integers, Least common multiple, Product of the gcd and the lcm

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