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 numbers is 54, what is the other number?

(a) 36
(b) 45
(c) 9
(d) 81

Solution:

(d) 81
Let the two numbers be x and y.
It is given that:
x = 54
​HCF = 27
LCM = 162
We know,

$x \times y=\mathrm{HCF} \times \mathrm{LCM}$

$\Rightarrow 54 \times y=27 \times 162$

$\Rightarrow 54 y=4374$

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