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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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