Question : The least number that divides 37044, gives the result in a perfect cube, is:
Option 1: 2
Option 2: 4
Option 3: 14
Option 4: 21
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Correct Answer: 4
Solution : We have to find the smallest number that divides 37044 and results in a perfect cube. Here, 37044 = 2 × 2 × 3 × 3 × 3 × 7 × 7 × 7 = 4 × 33 × 73 = 4 × (21)3 Therefore, the smallest number that divides 37044 and results in a perfect cube is 4. Hence, the correct answer is 4.
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Question : The least number that should be subtracted from 63520 to make the result a perfect square is:
Option 1: 30
Option 2: 24
Option 4: 16
Question : Let $x$ be the least number which when subtracted from 10424 gives a perfect square number. What is the least number by which $x$ should be multiplied to get a perfect square?
Option 1: 3
Option 2: 2
Option 3: 6
Option 4: 5
Question : What is the smallest number by which 625 must be divided so that the quotient is a perfect cube?
Option 1: 25
Option 2: 5
Option 3: 2
Option 4: 3
Question : Find the least number divisible by 2, 3, 5, 6, 9, and 18 which is a perfect square.
Option 1: 900
Option 2: 400
Option 3: 144
Option 4: 3600
Question : The least six-digit number, which is a perfect square, is:
Option 1: 100489
Option 2: 10000
Option 3: 100256
Option 4: 100255
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