Program to find the common ratio of three numbers

Given a:b and b:c. The task is to write a program to find ratio a:b:c
Examples:

Input: a:b = 2:3, b:c = 3:4
Output: 2:3:4

Input: a:b = 3:4, b:c = 8:9
Output: 6:8:9

Learn About : Ratio and Proportions

Approach: The trick is to make the common term ‘b’ equal in both ratios. Therefore, multiply the first ratio by b₂ (b term of second ratio) and the second ratio by b₁.

Given: a:b₁ and b₂:c 
Solution: a:b:c = (a*b₂):(b₁*b₂):(c*b₁)
For example:
If a : b = 5 : 9 and b : c = 7 : 4, then find a : b : c.
Solution:
Here, Make the common term ‘b’ equal in both ratios. 
Therefore, multiply the first ratio by 7 and the second ratio by 9. 
So, a : b = 35 : 63 and b : c = 63 : 36 
Thus, a : b : c = 35 : 63 : 36

Below is the implementation of the above approach: 

6:8:9

Time Complexity : O(log(A+B)) ,where A=a*b2 and B = b1*b2

Space Complexity : O(1), since no extra space has been taken.