Question

If LCM of $a$ and $18$ is $36$ and the HCF of $a$ and $18$ is $2$, then the value of $a$ is _________.

Answer 1

Calculate the value of $a$ using the formula

We know that the relation between the HCF and the LCM of any two numbers $a$ and $b$ is given by,

$\mathrm{HCF}(\mathrm{a},\mathrm{b})\times \mathrm{LCM}(\mathrm{a},\mathrm{b})=a\times b$

It is given that, $\mathrm{LCM}(a,18)=36$

And, $\mathrm{HCF}(a,18)=2$

And, the numbers are $a$ and $18$.

Now, using the above formula,

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

$\Rightarrow$ $2\times 36=a\times 18$ $\left[\because \mathrm{HCF}(a,18)=2,\mathrm{LCM}(a,18)=36\right]$

$\Rightarrow$ $\frac{2\times 36}{18}=a$

$\Rightarrow$ $\frac{2\times 2}{1}=a$

$\Rightarrow$ $4=a$

Or, $a=4$

Hence, the required value of $a$ is $4$.