If two positive integers x and y are expressible
in terms of primes as x = p’q and y = p q,
what can you say about their LCM and
HCF? Is LCM a multiple of HCF? Explain.
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Answer:
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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If two positive integer x and y are expressible in the term of primes as x=p
2
q
3
and y=p
3
q what can you say about their LCM and HCF , is LCM is multiple of HCF ?
Easy
Solution
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x=p
2
q
3
,y=p
3
q
LCM=p
3
q
3
,HCF=p
2
q
Yes LCM is a multiple of HCF
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