Question

If $\mathrm{HCF}(18,72)=18$, then find the $\mathrm{LCM}(18,72)$.

Answer 1

Calculate the LCM

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, $\mathrm{HCF}(18,72)=18$

So, the numbers are $a=18$ and $b=72$

Now, using the above formula,

$\mathrm{HCF}(18,72)\times \mathrm{LCM}(18,72)=18\times 72$

$\Rightarrow$ $18\times \mathrm{LCM}(18,72)=18\times 72$ $\left[\because \mathrm{HCF}(18,72)=18\right]$

$\Rightarrow$ $\mathrm{LCM}(18,72)=\frac{18\times 72}{18}$

$\Rightarrow$ $\mathrm{LCM}(18,72)=\frac{1\times 72}{1}$

$\Rightarrow$ $\mathrm{LCM}(18,72)=72$

Hence, the required value of $\mathrm{LCM}(18,72)$ is $72$.