Greatest common divisor of fractions and decimals

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SUMMARY

The greatest common divisor (GCD) and least common multiple (LCM) are strictly defined for integers and cannot be directly applied to decimals or fractions. When considering positive rational numbers, a new definition is necessary: x divides y if y/x is an integer. This allows for the calculation of GCD and LCM for positive rational numbers, but without a clear definition, the concepts become ambiguous.

PREREQUISITES
  • Understanding of integers and their properties
  • Familiarity with the concepts of greatest common divisor and least common multiple
  • Basic knowledge of positive rational numbers
  • Ability to define mathematical terms and operations
NEXT STEPS
  • Research the definition and properties of positive rational numbers
  • Learn about the mathematical operations involving fractions
  • Explore alternative definitions of divisibility for non-integer numbers
  • Study the implications of GCD and LCM in number theory
USEFUL FOR

Mathematicians, educators, students studying number theory, and anyone interested in the properties of rational numbers and their mathematical operations.

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Is it possible to calculate the greatest common divisor of decimals and fractions? As far as I know, the greatest common divisor is a number you can calculate for integers, but I wonder if it's possible to calculate it for decimals and fractions.
 
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No. "Least common multiple" and "greatest common divisor" are only defined for integers. If you allow fractions or irrational numbers, then any number, other than 0, can be a "common multiple" or "common divisor" so there are no "least" or "greatest".
 
You will have to define divisor and multiple for this to work. One possibility: for positive rational numbers x,y, say x divides y if y/x is an integer. With this definition, gcd and lcm can be defined.
 

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