Question

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. $a^2{b}^2$
• C. $a^3{b}^2$
• D. $a^3{b}^3$

Answer 1

The correct option is C

$a^3{b}^2$

LCM:- Least common multiple is the product of the greatest power of each prime factor involved in the numbers.

Prime numbers:- It is a whole number greater than 1 whose only factors are 1 and itself. A factor is defined as a whole number that can be divided evenly into another number.

Exaplantion ofr the correct option:

Step 1: Given:

$p=a{b}^2$ and $q=a^{3}b$

Step 2: Finding the LCM of $(p,q)$:

Here, $p=ab²=a\times b\times b$ and $q=a³b=a\times a\times a\times b$

LCM of $p$ and $q$ $=$ LCM $(ab²,a³b)$

$$\begin{gathered} =a\times b\times b\times a\times a \\ =a³b² \end{gathered}$$

Thus, the LCM of $(p,q)$ is $a^3{b}^2$. Hence, option (c) is the correct option.