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Find out that smallest number which when multiplied by 8019 will make the quotient a perfect cube

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Answer:

This is research work

First 10 perfect cubes since we are asking for the smallest perfect cube:

1^3 = 1

2^3 = 8

3^3 = 27

4^3 = 64

5^3 = 125

6^3 = 216

7^3 = 343

8^3 = 512

9^3 = 729

10^3 = 1000

we divide 8019 by each of these perfect cubes

8019 / 1 = 8019

8019 / 8 = 1002.375

8019 / 27 = 297

8019 / 64 = 125.296875

8019 / 125 = 64,152

8019 / 216 = 37.15277777777778

8019 / 343 = 23.37900875

8019 / 512 = 15.66210938

8019 / 729 = 11

8019 / 1000 = 8.019

⇒the smallest number which, multiplied by 8019, will make the quotient a perfect cube: 27

⇒8019 divided by 27 gives an integer quotient of 297

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