import Mathlib

set_option maxHeartbeats 0

open BigOperators Real Nat Topology Rat

theorem mathd_numbertheory_530 (n k : ℕ) (h₀ : 0 < n ∧ 0 < k) (h₀ : (n : ℝ) / k < 6)
  (h₁ : (5 : ℝ) < n / k) : 22 ≤ Nat.lcm n k / Nat.gcd n k := by sorry