# The HCF of two numbers is 27 and their LCM is 162.

Question:

The HCF  of two numbers is 27 and their LCM is 162. If one of the number is 81, find the other.

Solution:

Let the two numbers be $x, y$.

It is given that:
x = 81
HCF = 27 and  LCM = 162

We know, Product of two numbers $=\mathrm{HCF} \times \mathrm{LCM}$

$\Rightarrow \quad x \times y=27 \times 162$

$\Rightarrow \quad 81 \times y=4374$

$\Rightarrow \quad y=\frac{4374}{81}=54$

Hence, the other number y is 54.