If two positive integers p and q can be expressed’
Question:

If two positive integers p and q can be expressed’ as p=ab2 and q = a3b; where 0, b being prime numbers, then LCM (p, q) is equal to

(a) ab

(b) a2b2

(c) a3b2

(d) a3b3

Solution:

(c) Given that, $p=a b^{2}=a \times b \times b$

and $\quad q=a^{3} b=a \times a \times a \times b$

$\therefore \quad$ LCM of $p$ and $q=$ 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 involved in the numbers]