show that if a1,a2,...,an are pairwise relatively prime integers, then [a1,a2,...,an] = a1a2...an

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- Jun 15th 2009, 07:44 PMsilentbobanother question
show that if a1,a2,...,an are pairwise relatively prime integers, then [a1,a2,...,an] = a1a2...an

- Jun 15th 2009, 09:39 PMBruno J.
You can first show it for two numbers $\displaystyle a,b$ 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.