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erastovalidia [21]
4 years ago
10

What is the smallest positive integer n for which

alt="n^{2}" align="absmiddle" class="latex-formula"> is divisible by 18 and n^{3} is divisible by 640?
Mathematics
1 answer:
11Alexandr11 [23.1K]4 years ago
7 0

Answer:

  120

Step-by-step explanation:

n^2 has a factor of 18, so factors of 3^2·2. Since n^2 is a perfect square, we know n must have a factor of 3·2 = 6.

n^3 has a factor of 640, so factors of 2^7·5. Since n^3 is a perfect cube, we know n must have a factor of 2^3·5 = 40.

The least common multiple of 6 and 40 is 120.

The smallest positive integer n is 120.

_____

<em>Check</em>

120^2/18 = 800

120^3/640 = 2700

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