Question
LCM of two numbers is 12 times their HCF. The product of
the numbers is 25920. What will be the maximum possible difference between the numbers?Solution
ATQ, Let HCF of two numbers be ‘x’ So, LCM of two numbers = 12 × x = 12x Or, x × 12x = 25920 Or, 12x² = 25920 Or, x² = 2160 Or, x = √2160 = 46.48 (Approx 46) LCM of two numbers = 46 × 12 = 552 Let two numbers be ‘46a’ and ‘46b’, where ‘a’ and ‘b’ are co-prime numbers. So, 46ab = 552 Or, a × b = 12 So, when a = 1 and b = 12, then difference will be maximum Desired difference = 46 × 12 – 46 × 1 = 506
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