Question

If $\mathrm{LCM}(\mathrm{x},18)=36$ and $\mathrm{HCF}(\mathrm{x},18)=2$, then $\mathrm{x}$ is

• A. $2$
• B. $3$
• C. $4$
• D. $5$

Answer 1

The correct option is C

$4$

Step 1: Explanation for correct option.

For option (C): $4$

We know that the product of two numbers is equal to the product of their LCM and HCF.

So, for the given two numbers $\mathrm{x}$ and $18$,

$\mathrm{x}$$\times 18=$$\mathrm{LCM}(\mathrm{x},18)\times$$\mathrm{HCF}(\mathrm{x},18)$

$\Rightarrow$$\mathrm{x}$$\times 18=$$36\times 2$

$\Rightarrow$ $\mathrm{x}$$=$$2\times 2$

$\Rightarrow$ $\mathrm{x}$$=$$4$

So, option C is correct

Step 2: Explanation for incorrect option.

For option (A): $2$

If $\mathrm{x}$$=$$2$, then LCM of $2$ and $18$ is $2\times 3\times 3=18$, which is not equals to $36$.

So, option A is incorrect

For option (B): $3$

If $\mathrm{x}$$=$$3$, then LCM of $3$ and $18$ is $2\times 3\times 3=18$, which is not equals to $36$.

So, option B is incorrect

For option (D): $5$

If $\mathrm{x}$$=$$5$, then LCM of $5$ and $18$ is $2\times 3\times 3\times 5=90$, which is not equals to $36$.

So, option D is incorrect

Thus, options (A), (B) and (D) are not correct.

Hence, the correct option is (C).