Express \(2250\) as the product of its prime factors.[1]
The number \(\dfrac{2250h}{k}\), where \(h\) and \(k\) are integers, is a perfect cube. Find the smallest positive integer value of \(h\) and of \(k\).[1]
Find two smallest possible integers, one is odd and the other is even, such that they have a lowest common multiple of \(2250\) and a highest common factor of \(45\).[2]
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