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MathNet 2023-part-07 — 187 problems (EN–VI) Question 84

Math Olympiad Vault · MathNet 2023-part-07 — 187 problems (EN–VI)

Question 84

Suppose $a$ and $b$ be positive integers not exceeding $100$ such that
$$
a b = \left(\frac{\operatorname{lcm}(a, b)}{\operatorname{gcd}(a, b)}\right)^2
$$
Compute the largest possible value of $a + b$.