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formal statement (Lean)
23theorem gcd_mul_lcm (a b : ℕ) : Nat.gcd a b * Nat.lcm a b = a * b := by
proof body
Term-mode proof.
24 exact Nat.gcd_mul_lcm a b
25
26/-! ### Casted lcm formulas (for analytic work) -/
27
28/-- A casted form of `gcd_mul_lcm`:
29\[
30(\gcd(a,b) : \mathbb{Q}) \cdot (\operatorname{lcm}(a,b) : \mathbb{Q}) = (a b : \mathbb{Q}).
31\]
32-/
used by (6)
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depends on (9)
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