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):
Product of two numbers=HCF×LCM
Let the other unknown number be x.
Given:

HCF=13

LCM=1989

First number=117

Substituting the values into our formula:

117×x=13×1989
x=
117
13×1989
​

Simplifying the fraction step-by-step:
Since
13
117
​
=9:

x=
9
1989
​

x=221
Thus, the second number is 221.