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Question
The least number by which 72 be multiplied to make it a perfect cube is ______.
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Solution
The least number by which 72 be multiplied to make it a perfect cube is 3.
Explanation:
Resolving 72 into prime factors, we get
72 = 2 × 2 × 2 × 3 × 3
Grouping the factors in triplets of equal factors, we get
72 = (2 × 2 × 2) × 3 × 3
We find that 2 occurs as a prime factor of 72 thrice, but 3 occurs as a prime factor only twice.
Thus, if we multiply 72 by 3, 3 will also occurs as a prime factor thrice and the product will be 2 × 2 × 2 × 3 × 3 × 3, which is a perfect cube.
Hence, the least number, which should be multiplied with 72 to get perfect cube, is 3.
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