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  "body": "\n## Statement\n\nLet $a$ and $b$ be natural numbers.\nThen $\\gcd(a, b) \\cdot \\operatorname{lcm}(a, b) = a b$, where $\\gcd$ is the [[greatest common divisor|02WF878BH1]] and $\\operatorname{lcm}$ is the [[least common multiple|09S5SN35DJ]].\n\n## Remarks\n\nFor integers $a$ and $b$ of any sign, the same argument gives $\\gcd(a, b) \\cdot \\operatorname{lcm}(a, b) = |a b|$.\nThus $\\operatorname{lcm}(a, b) = a b / \\gcd(a, b)$ when $a$ and $b$ are not both $0$. This is the usual way to compute the lcm, with the [[Euclidean algorithm|0TRNT4X7J0]].\nFor example, $\\gcd(4, 6) = 2$, $\\operatorname{lcm}(4, 6) = 12$ and $2 \\cdot 12 = 24 = 4 \\cdot 6$.\n\n## Explanations\n\n### L1 human\n\nThink of the prime factors of $a$ and $b$. The gcd takes, for each prime, the smaller of the two exponents, and the lcm takes the larger one.\nThe smaller exponent plus the larger exponent is the sum of the two exponents.\nSo the product of the gcd and the lcm has the same prime factors as $a b$.\n",
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