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. Is LCM a multiple of HCF? Explain.

Answer 1

Solution:
x = p²q³ and y = p³q
HCF(x, y) = p² x q
LCM(x, y) = p³ x q³
LCM(x, y) = (p x q²) x HCF(x, y)
=> LCM is a multiple of HCF.