Question
Two numbers have a sum of their LCM and HCF equal to
464, and their LCM is 28 times their HCF. One of the numbers is 64. Find the difference between the two numbers.Solution
Let the HCF of the numbers = x LCM of the numbers = 28x According to the question, 28x + x = 464 Or, 29x = 464 Or, x = 16 HCF of the numbers = 16 LCM of the numbers = 28 × 16 = 448 As we know, Product of two numbers = product of their LCM and HCF Or, 64 × second number = 16 × 448 Or, second number = {(16 × 448)/64} = 112 Required difference between the numbers = 112 – 64 = 48
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