Hi, I need some help proving that the below formula is true.
It says: Use the Fundamental Theorem of Arithmetic to prove the following formula connecting GCD and LCM for three integers.
[a, b, c] = abc(a, b, c) / (b, c)(c, a)(a, b)
Now I know that FTA says that any integer has a unique decomposition of primes. And I know you can write any two integers as a decomposition of the same primes, with some powers that possibly equal 0.
How can I use this to prove the formula? Please help.