Problem Link - GCD and LCM Practice Problem in Basic Math
Problem Statement:
Two integers A and B are the inputs. Write a program to find GCD and LCM of A and B.
Approach:
- GCD: It is the largest integer that divides both A and B without leaving a remainder.
- LCM: It is the smallest positive integer that is divisible by both A and B.
- GCD(A, B): Can be calculated using the Euclidean Algorithm - Euclid Algorithm in Number theory
- LCM(A, B): Can be derived from the formula:
\text{LCM}(A, B) = \frac{A \times B}{\text{GCD}(A, B)}
Refer to this: GCD - LCM Relationship in Number theory
This formula works because the product of the GCD and LCM of two numbers is equal to the product of the numbers themselves.
Complexity:
- Time Complexity: The time complexity of the Euclidean algorithm is
O(log(min(a,b))). For calculating lcm it requiresO(1). - Space Complexity:
O(1)No extra space required.