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Let $x$ and $y$ be two distinct prime numbers and $p = x^2 y^3$, $q = xy^4$, $r = x^5 y^2$. Find the HCF and LCM of $p, q$ and $r$. Further check if HCF $(p, q, r) \times$ LCM $(p, q, r) = p \times q \times r$ or not.
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$p = x^2y^3, q = xy^4, r = x^5y^2$
HCF $(p,q,r) = xy^2$
LCM $(p,q,r) = x^5y^4$
HCF $\times$ LCM $= x^6y^6$
$p \times q \times r = x^8y^9$
$\Rightarrow$ HCF $(p, q, r) \times$ LCM $(p, q, r) \neq p \times q \times r$
HCF $(p,q,r) = xy^2$
LCM $(p,q,r) = x^5y^4$
HCF $\times$ LCM $= x^6y^6$
$p \times q \times r = x^8y^9$
$\Rightarrow$ HCF $(p, q, r) \times$ LCM $(p, q, r) \neq p \times q \times r$