Question

if two positive integers x and y are expressible in terms of primes as x = p²q³ and y = p³q, what can you say about their lcm and hcf?​

Answer 1

Given that,

• x = p²q³
• y = p³q¹

HCF = product of lowest common powers.

Therefore, HCF(x, y) = p²q

LCM = product of highest powers.

Therefore, LCM(x, y) = (pq)³.

More: $HCF(x, y) | LCM(x, y)$.

{I.e., for any numbers, HCF is a factor of LCM.}