Question:
If two positive ingeters $a$ and $b$ are expressible in the form $a=p q^{2}$ and $b=p^{3} q ; p, q$ being prime number, then LCM ( $a$,b) is
(a) $p q$
(b) $p^{3} q^{3}$
(c) $p^{3} q^{2}$
(d) $p^{2} q^{2}$
Solution:
Two positive integers are expressed as follows:
$a=p q^{2}$
$b=p^{3} q$
p and q are prime numbers.
Then, taking the highest powers of p and q in the values for a and b we get:
$\operatorname{LCM}(a, b)=p^{3} q^{2}$
Hence the correct choice is (c).
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