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Smallest x

Source: AHSME 1963 Problem 8

January 9, 2014
number theoryprime factorizationAMC

Problem Statement

The smallest positive integer xx for which 1260x=N31260x=N^3, where NN is an integer, is:
<spanclass=′latex−bold′>(A)</span> 1050<spanclass=′latex−bold′>(B)</span> 1260<spanclass=′latex−bold′>(C)</span> 12602<spanclass=′latex−bold′>(D)</span> 7350<spanclass=′latex−bold′>(E)</span> 44100<span class='latex-bold'>(A)</span>\ 1050 \qquad <span class='latex-bold'>(B)</span>\ 1260 \qquad <span class='latex-bold'>(C)</span>\ 1260^2 \qquad <span class='latex-bold'>(D)</span>\ 7350 \qquad <span class='latex-bold'>(E)</span>\ 44100
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