#include <bits/stdc++.h>
#define SYN ios_base::sync_with_stdio(0);cin.tie(0);
using namespace std;
/***************************************************************************************************************************************/
typedef long long int LLI;
typedef unsigned long long int ULLI;
#define IMAX ((unsigned)1<<31)-1
#define eps 1e-11
#define LIMAX (1LL<<63)-1
#define ULIMAX (1LL<<64)-1
#define UIMAX ((LLI)1<<32)-1
#define MP(X,Y) make_pair(X,Y)

#define REP(i,n) for(int i=0;i<n;i++)
#define DREP(i,n) for(int i=n;i>=0;i--)
#define LREP(i,a,b) for(int i=a;i<=b;i++)
#define DLREP(i,a,b) for(int i=a;i>=b;i--)
#define FOR(i,a,b,c) for(int i=a;i<=b;i+=c)

#define fill(a,v) memset(a,v,sizeof(a))
#define DEBUG(x) cout << #x << ": " << x << endl;
#define SZ(X) ((int)X.size())
#define all(x) (x).begin(),(x).end()
#define SORT(x) sort(all(x))
#define VI vector<int>
#define VS vector<string>
#define PB push_back
#define REV(a) reverse(all(a))
typedef pair<int, int>PII;
typedef pair<LLI, LLI>PLL;
typedef pair<char, int>PCI;
typedef pair<int, char>PIC;
typedef pair<double, double>PDD;
#define MSI map<string,int>
#define MSLI map<string,LLI>
#define MCI map<char,int>
template<class T> inline T MIN_3(T a, T b, T c)
{
    return min(min(a, b), c);
}
template<class T> inline T MAX_3(T a, T b, T c)
{
    return max(max(a, b), c);
}
#define ACM(x) accumulate(all(x),0);
#define CAP(x,y,z) set_intersection (all(x), all(y), z.begin())
#define CUP(x,y,z) set_union(all(x),all(y),z.begin())
#define DIF(x,y,z) set_difference (all(x),all(y),z.begin());
#define BRPS(n,bit) bitset<bit>(n)
#define DSORT(X)  sort(X.rbegin(), X.rend());
#define read(x) freopen(#x".txt","r",stdin)
#define write(x) freopen(#x".txt","w",stdout)
#define LB(A, x) (lower_bound(all(A), x) - A.begin())//exactly where it starts
#define UB(A, x) (upper_bound(all(A), x) - A.begin())
#define UNQ(x) SORT(x),(x).erase(unique(all(x)),x.end())

template<class T> inline T BIGMOD(T n, T m, T mod)
{
    LLI ans = 1;
    LLI k = n;
    while(m)
    {
        if(m & 1)
        {
            ans *= k;
            if(ans>mod) ans %= mod;
        }
        k *= k;
        if(k>mod) k %= mod;
        m >>= 1;
    }
    return ans;
}


inline int DBLCMP(double a, double b)
{
    if(fabs(a - b) <= eps) return 0;
    if(a < b) return -1;
    return 1;
}
template<class T> inline T sqr(T x)
{
    return x*x;
}
template<class T> inline int countbit(T n)
{
    return (n == 0) ? 0 : (1 + countbit(n&(n - 1)));
}
template<class T> inline T euclide(T a, T b, T &x, T &y)
{
    if (a < 0)
    {
        T d = euclide(-a, b, x, y);
        x = -x;
        return d;
    }
    if (b < 0)
    {
        T d = euclide(a, -b, x, y);
        y = -y;
        return d;
    }
    if (b == 0)
    {
        x = 1;
        y = 0;
        return a;
    }
    else
    {
        T d = euclide(b, a % b, x, y);
        T t = x;
        x = y;
        y = t - (a / b) * y;
        return d;
    }
}
template<class T> string toString(T n)
{
    ostringstream ost;
    ost << n;
    ost.flush();
    return ost.str();
}
template<class T> string toBinary(T n)
{
    string ret="";
    while(n)
    {
        if(n%2==1)ret+='1';
        else ret+='0';
        n>>=1;
    }
    reverse(ret.begin(),ret.end());
    return ret;
}
void combination(int n,vector< vector<int> > &ret)
{
    ret.resize(n+1, vector<int>(n+1, 0));
    for(int i=1; i<=n; i++)
    {
        ret[i][0]=ret[i][i]=1;
        for(int j=1; j<i; j++)
        {
            ret[i][j]=ret[i-1][j]+ret[i-1][j-1];
        }
    }
}
int toInt(string s)
{
    int r = 0;
    istringstream sin(s);
    sin >> r;
    return r;
}
LLI toLInt(string s)
{
    LLI r = 0;
    istringstream sin(s);
    sin >> r;
    return r;
}
double toDouble(string s)
{
    double r = 0;
    istringstream sin(s);
    sin >> r;
    return r;
}
vector<string> parse(string temp)
{
    vector<string> ans;
    ans.clear();
    string s;
    istringstream iss(temp);
    while (iss >> s)ans.PB(s);
    return ans;
}
template<class T> inline T gcd(T a, T b)
{
    if (a < 0)return gcd(-a, b);
    if (b < 0)return gcd(a, -b);
    return (b == 0) ? a : gcd(b, a % b);
}
template<class T> inline T lcm(T a, T b)
{
    if (a < 0)return lcm(-a, b);
    if (b < 0)return lcm(a, -b);
    return a*(b / gcd(a, b));
}
template<class T> inline T power(T b, T p)
{
    if (p < 0)return -1;
    if (b <= 0)return -2;
    if (!p)return 1;
    return b*power(b, p - 1);
}
#define fst first
#define snd second
//istringstream(temp) >> data >> value >> stamp;
//mod1 = 1000000007, mod2 = 1000000009;
//.016-.040-.900-2.48
/***************************************************************************************************************************************/
#define sqr 320
#define Mx (317*317)
bool chk[Mx];
VI primes;

void sieve()
{
    for(int i=2; i<=sqr; i++)
    {
        if(!chk[i])
        {
            for(int j=i+i; j<Mx; j+=i)
            {
                chk[j]=true;
            }
        }
    }
    primes.PB(2);
    for(int i=3;i<Mx;i+=2)if(!chk[i])primes.PB(i);
}
int N,K;
VI V;
int mem[5111];
int psz;

map<int,bool>bad;
int fu(int N)
{
    int ct=0;
    int ret=0;
    //int mid=sqrt(N);
    REP(i,psz)
    {
        //if(primes[i]>mid)break;
        ct=0;
        while(N%primes[i]==0)
        {
            N/=primes[i];
            ct++;
        }
        if(ct)
        {
            if(bad.find(primes[i])==bad.end())
            {
                ret+=ct;
            }
            else
            {
                ret-=ct;
            }
            //mid=sqrt(N);
        }
        if(N==1)break;
    }
    if(N!=1)
    {
        if(bad.find(N)==bad.end())ret++;
        else ret--;
    }
    return ret;
}
int benifit(int n)
{
    if(n==1)return 0;
    return fu(n);
}
VI Div;
int sum[5111];
int main()
{
    sieve();
    psz=primes.size();
    scanf("%d %d",&N,&K);
    V.resize(N);
    int x;
    REP(i,N)scanf("%d",&V[i]);
    REP(i,K){scanf("%d",&x);bad[x]=true;}
    int g=V[0];
    for(int i=0;i<N;i++)
    {
        g=gcd(g,V[i]);
        Div.PB(g);
    }
    int uu=0;
    REP(i,N)
    {
        uu+=fu(V[i]);
    }
    int res=0;
//    for(int i=N;i>0;--i){
//
//        x = V[0];
//
//        for(int j=0;j<i;++j)
//            x = gcd(x,V[j]);
//
//        if(benifit(x) < 0){
//            for(int j=0;j<i;++j)
//                V[j] /= x;
//        }
//    }
    for(int i=Div.size()-1;i>=0;i--)
    {
        //cout << "# " << div[i] << benifit(div[i]) << endl;
        int ben=benifit(Div[i]);
        if(ben<0)
        {
            for(int j=i;j>=0;j--)
            {
                V[j]/=gcd(V[j],Div[i]);//******************************.........................
                Div[j]/=gcd(Div[j],Div[i]);//****************************.......................
            }
        }
    }
    res=0;
    REP(i,N)res+=fu(V[i]);
    //cout << uu << " : " << max(res,uu) << endl;
    cout << max(res,uu) << endl;
    return 0;
}