CBSE Class 10 Maths (Standard) 2025 · Paper 30/4/1 · Question 26(b)

Real Numbers 3 marks Medium

Let

x

and

y

be two distinct prime numbers and

p = x^{2} y^{3}, q = x y^{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.

Answer

HCF (p, q, r) = x y^{2}

and

LCM (p, q, r) = x^{5} y^{4}

; since

HCF \times LCM = x^{6} y^{6}

while

p \times q \times r = x^{8} y^{9}

, the relation does not hold.

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