All-Russian Regional Preparation NT Exercise 1

Natural numbers $a, b, c$ are such that $abc = 60000000$. What is the largest possible value of $\gcd(a, b, c)$?

Replace sorry in the template below with your solution. See Answer Bank for acceptible answer declarations. Mathlib version used by the checker is v4.29.0.

import Mathlib.Algebra.GCDMonoid.Multiset
import Mathlib.Algebra.GCDMonoid.Nat
import Mathlib.Order.Bounds.Defs

def answer : ℕ := sorry

theorem solution : IsGreatest
    {g | ∃ a b c : ℕ, a * b * c = 60000000 ∧ Multiset.gcd {a, b, c} = g} answer := sorry

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