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  "aliases": [
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  "body": "\n## Definition\n\nLet $a$ and $b$ be nonzero integers.\nA common multiple of $a$ and $b$ is an integer $m$ such that $a \\mid m$ and $b \\mid m$.\nThe least common multiple $\\operatorname{lcm}(a, b)$ is the smallest positive common multiple of $a$ and $b$.\nBy convention, $\\operatorname{lcm}(a, 0) = \\operatorname{lcm}(0, a) = 0$ for each integer $a$.\n\n## Remarks\n\nThe positive integer $|a b|$ is a common multiple, so $\\operatorname{lcm}(a, b)$ exists and $\\operatorname{lcm}(a, b) \\le |a b|$.\nEach common multiple of $a$ and $b$ is a multiple of $\\operatorname{lcm}(a, b)$.\nFor example, $\\operatorname{lcm}(4, 6) = 12$.\nThe [[product of the gcd and the lcm|0TDY6JZHKS]] is the product of the two numbers.\n\n## Explanations\n\n### L1 human\n\nList the positive multiples of each number, and take the smallest number that is in both lists.\nThe multiples of $4$ are $4, 8, 12, 16, \\dots$ and the multiples of $6$ are $6, 12, 18, \\dots$.\nThus $\\operatorname{lcm}(4, 6) = 12$. You use this number when you add $\\tfrac{1}{4} + \\tfrac{1}{6}$ with a common denominator.\n",
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