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## Main Question or Discussion Point

Hi,

I encountered the following formula while reading, can anyone prove this:

[tex]lcm(a,b)=gcd(a^{-1},b^{-1})^{-1}[/tex]

Also, how could one do the gcd for non-integer?

for example we know that lcm(1/3,2/5)=2. then if we use the formula above then lcm(1/3,2/5)=1/gcd(3,5/2). then gcd(3,5/2) should be 1/2 but it does not make sense (to me at least).

Can anyone explain? Is this depends on which integral domain and its field of fractions that we work on?

I encountered the following formula while reading, can anyone prove this:

[tex]lcm(a,b)=gcd(a^{-1},b^{-1})^{-1}[/tex]

Also, how could one do the gcd for non-integer?

for example we know that lcm(1/3,2/5)=2. then if we use the formula above then lcm(1/3,2/5)=1/gcd(3,5/2). then gcd(3,5/2) should be 1/2 but it does not make sense (to me at least).

Can anyone explain? Is this depends on which integral domain and its field of fractions that we work on?