Easy as... 3.14?

by shiningsunnyday, Dec 3, 2016, 2:57 PM

Combo 3 homework (Medium) wrote:
Let $a_1, a_2, \ldots, a_n$ be positive integers. Prove that $$\text{lcm}(a_1, a_2, \ldots, a_n)=\frac{a_1 \cdot a_2 \cdots a_n}{\gcd(a_1, a_2) \cdot \gcd(a_1, a_3) \cdots \gcd(a_{n-1}, a_n)} \cdot \frac{\gcd(a_1, a_2, a_3) \cdots}{\gcd(a_1, a_2, a_3, a_4) \cdots} \cdots .$$
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To share with readers my favorite problem I came across today :) (Shout for contrib.)

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