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  "body": "\n## Statement\n\nLet $a$ and $b$ be natural numbers that are [[coprime|0GFKP8F8AG]].\nThen $\\operatorname{lcm}(a, b) = a b$.\n\n## Remarks\n\nThis follows from the [[product of the gcd and the lcm|0TDY6JZHKS]], because $\\gcd(a, b) = 1$.\nThe converse is also true when $a$ and $b$ are positive: if $\\operatorname{lcm}(a, b) = a b$, then $a$ and $b$ are coprime.\nFor example, $\\operatorname{lcm}(8, 15) = 120$.\n\n## Explanations\n\n### L1 human\n\nWhen $a$ and $b$ have no common factor, a multiple of both must contain all the factors of $a$ and all the factors of $b$.\nNo factor can serve both numbers at the same time, so the smallest common multiple is $a b$.\n",
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