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GCD & LCMhard
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Find the number of ordered pairs of positive integers (a,b)(a, b)(a,b) such that LCM(a,b)=23⋅32⋅51\text{LCM}(a, b) = 2^3 \cdot 3^2 \cdot 5^1LCM(a,b)=23⋅32⋅51 and GCD(a,b)=21⋅31\text{GCD}(a, b) = 2^1 \cdot 3^1GCD(a,b)=21⋅31.