show that if a1,a2,...,an are pairwise relatively prime integers, then [a1,a2,...,an] = a1a2...an
You can first show it for two numbers and then use induction to show it for arbitrary sets of pairwise relatively prime integers.
Hint : you could use the representation of any integer as a product of powers of primes. How can you determine the G.C.D. and the L.C.M of two numbers using this representation?
There is a particular formula linking the GCD and the LCM, which I'm sure you can figure out.