Question

Let x and y be two distinct prime numbers, and p = x²y³, q = xy⁴, r = x⁵y². Find the HCF and LCM of p, q, and r. Further check if HCF (p, q, r) × LCM (p, q, r) = p × q× r or not.

Answer 1

Given: p = x²y³, q = xy⁴, r = x⁵y²

HCF (p, q, r) = x¹y² = xy²

The HCF is obtained by multiplying the common prime factors raised to their lowest powers.

LCM (p, q, r) = x⁵y⁴

p × q × r = x²y³ × xy⁴ × x⁵y²

= x⁸y⁹

According to the question,

HCF (p, q, r) × LCM (p, q, r)

= xy² × x⁸y⁹

= x⁹y¹¹

≠ p, q, r

HFC (p, q, r) × LCM (p, q, r) = p × q × r