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LCM triples

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March 16, 2006
number theoryleast common multiplesymmetryAMCAIME

Problem Statement

Let [r,s][r,s] denote the least common multiple of positive integers rr and ss. Find the number of ordered triples (a,b,c)(a,b,c) of positive integers for which [a,b]=1000[a,b] = 1000, [b,c]=2000[b,c] = 2000, and [c,a]=2000[c,a] = 2000
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