Question
LCM of two numbers is 10 times their HCF. The product of
the numbers is 18000. What will be the maximum possible difference between the numbers?Solution
ATQ, Let HCF of two numbers be ‘x’ So, LCM of two numbers = 10 × x = 10x Or, x × 10x = 18000 Or, 10x² = 18000 Or, x² = 1800 Or, x = √1800 = 42.43 (Approx 42) LCM of two numbers = 42 × 10 = 420 Let two numbers be ‘42a’ and ‘42b’, where ‘a’ and ‘b’ are co-prime numbers. So, 42ab = 420 Or, a × b = 10 So, when a = 1 and b = 10, then difference will be maximum Desired difference = 42 × 10 – 42 × 1 = 378
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