lcm(2, 2, 2) * gcd(2, 2, 2) != 2*2*2

This formula isn't correct. For example, a1 = 2, a2 = 4, a3 = 5. LCM(a1,a2,a3) = 20, GCD(a1,a2,a3) = 1, a1*a2*a3 = 40. And LCM(a1,a2,a3) * GCD(a1,a2,a3) != a1*a2*a3.

i have used the same concept.... for calculating the lcm of first 20 natural numbers my code is as follows... but the answer is not coming correct

int gcd(int a, int b)
{
    if(b==0)
    return a;
    else
    return gcd(b,a%b);
}
int lcm(int a,int b)
{
    return a*b/gcd(a,b);
}

int main()
{
    int ans=2;
    for(int i=3;i<=20;i++)
    {
        ans= lcm(ans,i);
    }
    cout<<ans<<"\n";
    return 0;
}