Question

If two positive integer a and b are written as a = x to
the power 3.y to the power 2 and b = x.y to the power3;
x, y are prime numbers, then HCF (a, b) is​

Answer 1

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

Step-by-step explanation:

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