Question

What is the smallest positive integer $n$ for which $n^2$ is divisible by 18 and $n^3$ is divisible by 640

Answer 1

The smallest positive integer n for which n^2 is divisible by 18 and n^3 is divisible by 640 is 120

The modulo (or "modulus" or "mod") is the remainder after dividing one number by another.

The smallest integer is 120, since:

$120^{2}$ mod 18 = 0, (reminder after dividing $120^{2}$ by 18 is 0) and

$120^{3}$ mod 640 = 0 (reminder after dividing $120^{3}$ by 18 is 0)

Hence, The smallest positive integer n for which n^2 is divisible by 18 and n^3 is divisible by 640 is 120.

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