LCM of Two Numbers in C++

LCM in C++ is (a × b) / GCD. LCM(12, 18) is 36. Save a and b before Euclid.

IntermediateLoop ProgramsExample 6 of 14

lcm-of-two-numbers.cpp

1#include <iostream>
2using namespace std;
3
4int main() {
5    int a, b, gcd, lcm;
6    
7    cout << "Enter two numbers: ";
8    cin >> a >> b;
9    
10    int originalA = a, originalB = b;
11    
12    // Find GCD first
13    while (b != 0) {
14        int temp = b;
15        b = a % b;
16        a = temp;
17    }
18    gcd = a;
19    
20    // LCM = (a * b) / GCD
21    lcm = (originalA * originalB) / gcd;
22    
23    cout << "LCM of " << originalA << " and " << originalB << " is: " << lcm << endl;
24    
25    return 0;
26}

Output

Enter two numbers: 12 18
LCM of 12 and 18 is: 36

What's going on

LCM is the smallest positive integer both numbers divide. LCM(12, 18) is 36. Don't list multiples — use LCM = (a × b) / GCD.

cin >> a >> b;

int originalA = a, originalB = b;

The GCD loop eats a and b.

Same Euclid as the GCD program:

while (b != 0) { int temp = b; b = a % b; a = temp; }

gcd = a;

12 and 18 → GCD 6.

lcm = (originalA * originalB) / gcd;

(12 × 18) / 6 = 36. Use the originals. After the loop a is 6 and b is 0. (a * b) / gcd is 0.

Overflow: originalA * originalB can wrap before you divide. Safer: (originalA / gcd) * originalB when gcd divides originalA (it does). This program uses the textbook form.

Coprime pair: GCD(7, 5) = 1, LCM = 35. Equal pair: LCM(12, 12) = 12.

Sample print: LCM of 12 and 18 is: 36.

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