greatest common divisor of fractions and decimals

topito2

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.

HallsofIvy

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".

g_edgar

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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topito2	greatest common divisor of fractions and decimals Tweet 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.

HallsofIvy Recognitions: Gold Member Science Advisor Staff Emeritus	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".

g_edgar	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.