If two positive integers x and y are expressible in terms of primes as x = p^2q^3 and y = p^3q, what can you say about their LCM and HCF.
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.
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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.
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