# 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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