📐 GCD and LCM from Prime Factorisations
If $a = \\prod p_i^{\\alpha_i}$ and $b = \\prod p_i^{\\beta_i}$, then $\\gcd(a,b) = \\prod p_i^{\\min(\\alpha_i, \\beta_i)}$ and $\\text{lcm}(a,b) = \\prod p_i^{\\max(\\alpha_i, \\beta_i)}$.
From: intro-discrete
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