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  "body": "\n## Proof\n\n1. Let $a$ and $b$ be natural numbers that are [[coprime|0GFKP8F8AG]]. By definition, $\\gcd(a, b) = 1$.\n2. By the [[product of the gcd and the lcm|0TDY6JZHKS]], $\\gcd(a, b) \\cdot \\operatorname{lcm}(a, b) = a b$.\n3. Substituting $\\gcd(a, b) = 1$ gives $\\operatorname{lcm}(a, b) = a b$, where $\\operatorname{lcm}$ is the [[least common multiple|09S5SN35DJ]].\n\n## Idea\n\nThe gcd times the lcm is always the product. When the gcd is $1$, nothing is left to divide out, so the lcm is the product itself.\n",
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