Question
LCM of two numbers is 8 times their HCF. The product of
the numbers is 10240. What will be the maximum possible difference between the numbers?Solution
ATQ, Let HCF of two numbers be ‘x’ So, LCM of two numbers = 8 × x = 8x Or, x × 8x = 10240 Or, 8x² = 10240 Or, x² = 1280 Or, x = √1280 = 35.78 (Approx 36) LCM of two numbers = 36 × 8 = 288 Let two numbers be ‘36a’ and ‘36b’, where ‘a’ and ‘b’ are co-prime numbers. So, 36ab = 288 Or, a × b = 8 So, when a = 1 and b = 8, then difference will be maximum Desired difference = 36 × 8 – 36 × 1 = 252
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