Discussion
The LCM and HCF of two positive numbers is 1000 and 50 respectively. Which of the following could be the pair of such numbers?
Answer: D
The pair is 200 and 250.
For any two numbers, HCF \(\times\) LCM = product of the numbers, so the product must be \(50 \times 1000 = 50000\). Of the options, \(200 \times 250 = 50000\), and indeed HCF(200, 250) = 50 and LCM = 1000.
200 and 500 have HCF 100 and LCM 1000; 150 and 250 have HCF 50 but LCM 750; 50 and 100 have HCF 50 but LCM 100. Each fails one of the two conditions.
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