The LCM of two numbers is 864 and their HCF is 144. If one of the numbers is 288, what is the other number?

Use the relation:
Product of two numbers = LCM × HCF

So,
$288 \times \text{other number} = 864 \times 144$

Other number =
$\frac{864 \times 144}{288}$

Simplify:
$\frac{864}{288} = 3$

So,
$3 \times 144 = 432$

Final Answer: 432