The HCF and LCM of two numbers are $13$ and $1989$ respectively. If one of the numbers is $117$, then the other number is

We know the fundamental mathematical identity relating two numbers with their highest common factor (HCF) and lowest common multiple (LCM):
$$\text{Product of two numbers}=\text{HCF}\times \text{LCM}$$
Let the other unknown number be $x$.Given:$\text{HCF}=13$$\text{LCM}=1989$$\text{First number}=117$ Substituting the values into our formula:
$$117\times x=13\times 1989$$
$$x=\frac{13\times 1989}{117}$$
Simplifying the fraction step-by-step:Since $\frac{117}{13}=9$:
$$x=\frac{1989}{9}$$
$$x=221$$
Thus, the second number is $221$.