Question
The Least Common Multiple (LCM) of two numbers is 15
times their Highest Common Factor (HCF). The product of these two numbers is 15,360. What is the maximum possible difference between these numbers?Solution
Let HCF of two numbers be ‘x’ So, LCM of two numbers = 15 × x = 15x Or, x × 15x = 15360 Or, 15x2 = 15360 Or, x2 = 1024 Or, x = 32 LCM of two numbers = 32 × 15 = 480 Let two number be ‘32a’ and ‘32b’, where ‘a’ and ‘b’ are co-prime numbers. So, 32ab = 480 Or, a × b = 15 So, when a = 1 and b = 15, then difference will be maximum Desired difference = 32 × 15 – 32 × 1 = 448
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