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lcm_gcd.cpp
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59 lines (48 loc) · 1.25 KB
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// LCM and GCD
#include<iostream>
#include<cmath>
using namespace std;
// Euclidean algorithm to find GCD ( Greatest Common Divisor )
// gcd (a, b) = gcd(|a%b|, |a| ); where |a| >= |b|
// gcd(p, 0) = gcd(0, p) = |p|
// example : gcd(12, 18) = gcd(18%12, 12) = gcd(6,12) = gcd(12%6, 6) = gcd(0, 6) = 6
int gcd(int a , int b ){ // a is bigger , b is smaller
if(a==0 || b==0) return a+b;
else{
int absa = abs(a);
int absb = abs(b);
int bigVal = max(absa, absb);
int smallVal = min(absa, absb);
return gcd(bigVal%smallVal, smallVal);
}
}
int lcm(int a , int b){ // a is smaller , b is bigger
static int m = 0;
m+=b;
if((m%a == 0) && (m%b == 0))
return m;
else
lcm(a,b);
}
// approach 2 : Euclidean Algorithm
// lcm(a, b) = |a * b|/gcd(a, b).
int lcm2(int a, int b ){
return a*b / gcd(a,b);
}
int main(){
int a=4;
int b=6;
int gcdnum;
if(a>=b)
gcdnum = gcd(a,b);
else
gcdnum = gcd(b,a);
int lcmnum;
if(a<=b)
lcmnum = lcm(a,b);
else
lcmnum = lcm(b,a);
cout<< gcdnum << endl; //
cout<< lcmnum << endl; // lcm 4 and 6 should be 12
cout<< lcmnum << endl; // lcm 4 and 6 should be 12
}