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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