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Question
Find the least number by which 1323 must be multiplied so that the product is a perfect cube.
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Solution
1323 = 3 × 3 × 3 × 7 × 7
= 33 × 72
To make it a perfect cube, the power of each prime factor must be a multiple of 3.
The power of 3 is already 3, but the power of 7 is 2.
We need one more 7 to make it 73.
So, multiply 1323 by 7.
1323 × 7 = 9261
9261 is a perfect cube.
Therefore, the least number is 7.
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