Question

Find the HCF of $96$ and $404$ by prime factorization and use it to find the LCM.

Answer 1

Step 1: Find HCF by prime factorisation

HCF or the highest common factor of two numbers is the largest number which is a factor of both the numbers.

Prime factorise $96$ and $404$as follows:

$\begin{array}{rcl}96& =& 2\times 2\times 2\times 2\times 2\times 3\\ 404& =& 2\times 2\times 101\end{array}$

Common factors of $96$and $404$ are $2\times 2$

So, the highest common factor is $4$

Hence, HCF of $96$ and $404$ is $4$

Step 2: Calculate the LCM

We know that, LCM$\times$HCF $=$Product of two numbers

By the formula,

LCM $=\frac{96\times 404}{4}$ $[$$\because$HCF is $4]$

$\Rightarrow$ LCM $=96\times 101$

$\Rightarrow$ LCM $=9696$

Hence, LCM of $96$ and $404$ is $9696$ and the HCF is $4$.