Question

If $\mathrm{HCF}(336,54)=6$, then find the $\mathrm{LCM}(336,54)$.

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, $\mathrm{HCF}(336,54)=6$

So, the numbers are $a=336$ and $b=54$

Now, using the above formula,

$\mathrm{HCF}(336,54)\times \mathrm{LCM}(336,54)=336\times 54$

$\Rightarrow$ $6\times \mathrm{LCM}(336,54)=336\times 54$ $\left[\because \mathrm{HCF}(336,54)=6\right]$

$\Rightarrow$ $\mathrm{LCM}(336,54)=\frac{336\times 54}{6}$

$\Rightarrow$ $\mathrm{LCM}(336,54)=\frac{56\times 54}{1}$

$\Rightarrow$ $\mathrm{LCM}(336,54)=3024$

Hence, the required value of $\mathrm{LCM}(336,54)$ is $3024$.