Question

If p and q are positive integers such that p = ab² and q= a²b, where a , b are prime numbers, then the LCM (p, q) is

a) ab
b) a²b²
c) a³b²
d) a³b³​

Answer 1

Given,

$\[\begin{array}{l}p = a{b^2}\\q = {a^2}b\end{array}\]$

Solution,

Calculate the LCM of p and q.

$\[\begin{array}{l}p = a \times b \times b\\q = a \times a \times b\end{array}\]$

LCM ( p and q ),

$\[\begin{array}{l} = a \times a \times b \times b\\ = {a^2}{b^2}\end{array}\]$

Hence the LCM is $\[{a^2}{b^2}\]$

The correct option is (b), i.e. $\[{a^2}{b^2}\]$

Answer 2

a) ab.

Step-by-step explanation:

P = ab²    q = a²b

To Find:   LCM of (P,Q)

P = a × b × b

q = a × a × b

(p ,q)  = a × a × a × b × b × b.

Since a and b are prime Numbers.

⇒  Prime Number is the Numbers which is the multiple of 1 and itself.

⇒ so, a and b is the multiples of I and itself LCM is the least common Multiple.

By this

P = a × b × b

q =  a × a × b

Common Multiple of (p, q) is a × b ∴ LCM of (p , q) is ab.