The HCF of two numbers is 96 and their LCM is 1296. If one number is 864, then the other is:
A. 72
B. 64
C. 144
D. 11664

Answer Verified Verified
Hint: Here, we will substitute the values of HCF, LCM and one the formula \[{\text{HCF}} \times {\text{LCM}} = {\text{Product of two numbers}}\] to find the other number.

Complete step-by-step solution:
Given that the one number is 864.
Let us assume that the other number is n .

We know that the product of HCF and LCM is equal to the product of two numbers.

Now, we will find the other number using the above condition.

\[{\text{HCF}} \times {\text{LCM}} = {\text{Product of two numbers}}\]

Substituting the values of HCF, LCM and the both the numbers, we get

   \Rightarrow 96 \times 1296 = 864n \\
   \Rightarrow 124416 = 864n \\
   \Rightarrow \dfrac{{124416}}{{864}} = n \\
   \Rightarrow n = 144 \\

Thus, the other number is 144.

Hence, the option C is correct.

Note: In this question, we have to use the formula that the product of two numbers is equal to HCF and LCM. Also, we are supposed to write the values properly to avoid any miscalculation.