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GCD & LCMhard
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Find the number of positive integer pairs (a,b)(a, b)(a,b) such that a<ba < ba<b, gcd(a,b)=10\text{gcd}(a, b) = 10gcd(a,b)=10, and lcm(a,b)=1500\text{lcm}(a, b) = 1500lcm(a,b)=1500.