Ononot — For any three positive integers a, b, c, let g1 = \gcd(a,b),

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Divisibilityhard

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For any three positive integers $a, b, c$ , let $g_1 = \gcd(a,b)$ , $g_2 = \gcd(b,c)$ , and $g_3 = \gcd(c,a)$ . Which of the following expressions is always equivalent to the least common multiple $\operatorname{lcm}(a,b,c)$ ?