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Ethan

7. Two positive integers a and b can be written as a = xºy? and b = xy”,where x and y are prime numbers. Find HCF(a, b) and LCM(a, b).​

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Answer:

Given that a = x²y³ = x × x × x × y x y

b = xy³ = x × y × y × y

HCF of a and b would be

= (x³, y², xy³) = x × y × y

HCF = xy²

HCF is the product of the smallest power of each common prime factor involved in the numbers.

LCM = x³y³

LCM is the lowest common factor of each power.

HCF × LCM

xy² × x³y³

ab = x⁴y⁵

Thus: ab = HCF ₓ LCM

hope it helps

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