MCQ
Choose the correct answer from the given four options in the following questions:
If two positive integers $p$ and $q$ can be expressed as $p=a b^2$ and $q=a^3 b ; a, b$ being prime numbers, then LCM ( $p, q$ ) is:
  • A
    ab.
  • B
    . $a^2 b^2$.
  •  $a^3 b^2$.
  • D
    $a^3 b^3$.

Answer

Correct option: C.
 $a^3 b^2$.
Given that, $p = ab ^2= a \times b \times b$
and $q=a^3 b=a \times a \times a \times b$
$\therefore$ LCM of pandq $=\operatorname{LCM}\left(a b^2, a^3 b\right)=a \times b \times b \times a \times a=a^3 b^2$
(since, LCM is the product of the greatest power of each prime factor Invotved in the numbers)

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