Question

If $\mathrm{HCF}(a,8)=4,\mathrm{LCM}(a,8)=24$ then find the value of $a$.

Answer 1

Calculate the LCM using the formula:

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

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

It is given that, $\mathrm{HCF}(a,8)=4$

And, $\mathrm{LCM}(a,8)=24$

So, the numbers are $a$ and $b=8$

Now, using the above formula,

$\mathrm{HCF}(a,8)\times \mathrm{LCM}(a,8)=a\times 8$

$\Rightarrow$ $4\times 24=a\times 8$ $\left[\because \mathrm{HCF}(a,8)=4,\mathrm{LCM}(a,8)=24\right]$

$\Rightarrow$ $\frac{4\times 24}{8}=a$

$\Rightarrow$ $\frac{4\times 3}{1}=a$

$\Rightarrow$ $12=a$

Hence, the required value of $a$ is $12$.