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If two positive integers a and b are expressible in the form $a = p q^{2} and b = p^{3} q$ where p and q are prime numbers, then find $LCM (a, b)$ .

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p

p^{3} q^{3}

p^{2} q^{2}

p^{3} q^{2}

answer is C.

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Detailed Solution

It is given that two positive integers a and b are expressible in the form

a = p q^{2} and b = p^{3} q

where p and q are prime numbers.

a = p q^{2}

\Rightarrow a = p \times q \times q

b = p^{3} q

\Rightarrow b = p \times p \times p \times q

LCM (a, b) = q \times q \times p \times p \times p

\Rightarrow LCM (a, b) = p^{3} q^{2}

Therefore, if two positive integers a and b are expressible in the form

a = p q^{2} and b = p^{3} q

where p and q are prime numbers, then

LCM (a, b)

will be

p^{3} q^{2}

.
Hence, option 3 is correct.

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