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Question

Two positive integers a and b can be written as a = x3y2 and b = xy3, where x and y are prime numbers. Find HCF(a, b) and LCM(a, b).

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Solution

It is given that, a = x3y2 and b = xy3, where x and y are prime numbers.

LCMa, b=LCMx3y2, xy3 =The highest of indices of x and y =x3y3HCFa, b=HCFx3y2, xy3 =The lowest of indices of x and y =xy2

Hence, HCF(a, b) = xy2 and LCM(a, b) = x3y3.

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