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# The LCM of two numbers is 1200. Which of the following cannot be their HCF?A. 600B. 500C. 400D. 200

Last updated date: 23rd Jun 2024
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Hint: First we will define both the terms that are HCF and LCM with examples. After that we will draw a relation between both the terms by analyzing their properties and definition that HCF is a factor of LCM, then we will use the given data in the question to get the answer.

We have: $\text{LCM}=1200$ , now we will consider the options and see that 600,400,200 can be the HCF of the given two numbers as they are the factors of the LCM that means they divide it. Therefore, 500 cannot be the HCF of the given numbers.
Note: Students can make mistakes when they use the relation between HCF and LCM that the product of any two given numbers say x, y will be equal to product of their HCF and LCM. That is $xy=HCF\times LCM$ , here one cannot draw a final conclusion and no proper proof is there to support the statement given.