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 ?

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Solution

$x = p^{2} q^{3}, y = p^{3} q$
LCM is the product of highest powers of individual variables p and q, and
HCF is the product of lowest powers of the individual variable p and q.
Thus, $L C M = p^{3} q^{3}, H C F = p^{2} q$
Yes, $L C M$ is a multiple of $H C F$

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If two positive integer x and y are expressible in the term of primes as x=p2q3 and y=p3q what can you say about their LCM and HCF , is LCM is multiple of HCF ?

x=p2q3,y=p3qLCM is the product of highest powers of individual variables p and q, and HCF is the product of lowest powers of the individual variable p and q.Thus, LCM=p3q3,HCF=p2qYes, LCM is a multiple of HCF

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 ?

$x = p^{2} q^{3}, y = p^{3} q$
LCM is the product of highest powers of individual variables p and q, and
HCF is the product of lowest powers of the individual variable p and q.
Thus, $L C M = p^{3} q^{3}, H C F = p^{2} q$
Yes, $L C M$ is a multiple of $H C F$