Question
LCM of two numbers is 18 times their HCF. The product of
the numbers is 64800. What will be the maximum possible difference between the numbers?Solution
ATQ, Let HCF of two numbers be ‘x’ So, LCM of two numbers = 18 × x = 18x Or, x × 18x = 64800 Or, 18x² = 64800 Or, x² = 3600 Or, x = √3600 = 60 LCM of two numbers = 60 × 18 = 1080 Let two numbers be ‘60a’ and ‘60b’, where ‘a’ and ‘b’ are co-prime numbers. So, 60ab = 1080 Or, a × b = 18 So, when a = 1 and b = 18, then difference will be maximum Desired difference = 60 × 18 – 60 × 1 = 1020
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