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Question

The sum and difference of two numbers are 42 and 6 respectively. If the LCM of these two numbers is 72 , then the ratio of their HCF and LCM is?

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Solution

Let the numbers are x and y.According to question.x + y = 42 ......1x - y = 6 .....2Adding 1 and 2, we get2x = 48x = 24Now, from 1, we get y = 18So the two numbers are 24 and 18Now, LCM = 72HCF × LCM = product of 2 numbersLCM = product of 2 numbersHCF = 24 × 1872 = 6now,LCMHCF = 672 = 112

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