Question

The LCM of the smallest two-digit composite number and the smallest composite number is :

• A. $12$
• B. $4$
• C. $20$
• D. $44$

Answer 1

The correct option is C

$20$

Step 1: Calculating the prime factorization of composite numbers,

Here, the smallest two-digit composite number is $10$and the smallest composite number is $4$.

Prime factorizations of $10\mathrm{and}4$ are:

$$\begin{gathered} 10=2\times 5 \\ 4=2\times 2 \end{gathered}$$

Step 2: Calculating the LCM ( Least Common Multiple ) of the required numbers,

$\begin{array}{rcl}\mathrm{LCM}\left(4,10\right)& =& 2\times 2\times 5\\ & =& 20\end{array}$

Therefore, the required LCM is 20.

Final Answer:

Hence, the correct option is (c).