Track / Stage 4 / 59 of 340 #319 of 1964

Problem 319

AMC 12 late, AIME early

Number theory Difficulty 4.7 Find the answer

17. Determine the smallest positive integer $n$ such that $n$ is divisible by $20, n^{2}$ is a perfect cube, and $n^{3}$ is a perfect square.

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Official solution

17. 1000000

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.