Greatest common divisor of fractions and decimals

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The greatest common divisor (GCD) is traditionally defined only for integers, making it inapplicable to decimals and fractions without further definitions. If fractions or irrational numbers are considered, any non-zero number can serve as a common divisor or multiple, eliminating the concepts of "least" or "greatest." A proposed solution involves defining a divisor for positive rational numbers, where x divides y if y/x is an integer. This allows for the potential calculation of GCD and least common multiple (LCM) under this new framework. Therefore, while traditional GCD calculations do not extend to decimals and fractions, alternative definitions can facilitate their computation.
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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.
 
Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?

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