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What is the smallest positive integer n such that the fourth root of 56*n*360 is an integer?

 Apr 24, 2023
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56 * 360==20,160

 

20160 = 2^6 * 3^2 * 5 * 7

 

n==2^2 * 3^2 * 5^3 * 7^3 ==1,543,500

 

Check: 20,160  *  1,543,500==[31,116,960,000]^(1/4) ==420

 Apr 24, 2023

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