Question
LCM of two numbers is 5 times their HCF. The product of
the numbers is 4500. What will be the maximum possible difference between the numbers?Solution
ATQ, Let HCF of two numbers be ‘x’ So, LCM of two numbers = 5 × x = 5x Or, x × 5x = 4500 Or, 5x² = 4500 Or, x² = 900 Or, x = √900 = 30 LCM of two numbers = 30 × 5 = 150 Let two numbers be ‘30a’ and ‘30b’, where ‘a’ and ‘b’ are co-prime numbers. So, 30ab = 150 Or, a × b = 5 So, when a = 1 and b = 5, then difference will be maximum Desired difference = 30 × 5 – 30 × 1 = 120
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