1.

Write a program to calculate the Least Common Multiple (LCM) of two numbers. Example : Input : a = 10, b =15 Output : 30 a = 5, b = 7 Output : 35

Answer»

Input :
a = 10, b =15
Output :
30
a = 5, b = 7
Output :
35

Approach:

Let us assume the two numbers are a and b. Then, the two numbers have the following relationship :

 a * b = LCM(a, b) * GCD(a, b)

or,

 LCM(a, b) = (a * b) / GCD(a, b)

Let us take an example to UNDERSTAND better. For a = 10 and b = 15, a * b = 150, LCM(10, 15) = 30, GCD(10, 15) = 5. So, a * b = LCM(a, b) * GCD(a, b).

Code :

 #include <iostream>using namespace std; //Function to find the GREATEST common divisor of the two numbersint findGCD(int a,int b){ if (b == 0) return a; return findGCD(b, a % b);} // Function to return LCM of two numbersint findLCM(int a, int b){ return (a * b) / findGCD(a, b);} int MAIN(){ int a = 10, b = 15; cout <<"The Least Common Multiple of the two numbers " << a << " and " << b << " is : " << findLCM(a, b); return 0;}

Output:

 The Least Common Multiple of the two numbers 10 and 15 is : 30

Explanation: 

In the above code, the function findGCD() finds the greatest common divisor of the two numbers a and b. We use the Euclidean algorithm to find the greatest common divisor of the two numbers. The function findLCM() finds the least common multiple of the two numbers.


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