- #1
rukawakaede
- 59
- 0
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?