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GCD & LCMhard
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What is the smallest positive integer nnn such that gcd(n,12)=1\text{gcd}(n, 12)=1gcd(n,12)=1, gcd(n+1,12)=1\text{gcd}(n+1, 12)=1gcd(n+1,12)=1, and gcd(n+2,12)=1\text{gcd}(n+2, 12)=1gcd(n+2,12)=1?