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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:
[tex]120^{2}[/tex] mod 18 = 0, (reminder after dividing [tex]120^{2}[/tex] by 18 is 0) and
[tex]120^{3}[/tex] mod 640 = 0 (reminder after dividing [tex]120^{3}[/tex] 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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