# If two positive ingeters a and b are expressible in the form

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 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).