Not gonna lie

Consider all pairs of positive integers \((G, L ) \) such that \( 2 \leq G \leq L \leq 1000 \). For each pair, let there be \( N_{G, L} \) ordered pairs of positive integers \( (a, b) \) such that \( G = \gcd (a,b) \) and \( L = lcm(a,b) \).

What is the largest possible value of \( N_{G,L} \)?

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