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HMMT November 2023 T6

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The pairwise greatest common divisors of five positive integers are

2,3,4,5,6,7,8,p,q,r2,3,4,5,6,7,8, p, q, r

in some order, for some positive integers p,q,rp, q, r. Compute the minimum possible value of p+q+rp+q+r.

Dataset text NuminaMath olympiads. Quoted with source.

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