By what smallest number should 18252 be multiplied so that the product becomes a perfect cube?
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For a number to be a perfect cube, each of its prime factors has to have a power that is a multiple of 3. The prime factors that we need to "fix" then are 2 and 13, whose powers are 2. So we need to multiply by 2 × 13 = 26. The resulting perfect cube is 18252 × 26 = 2³ × 3³ × 13³ = 78³
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