#line 1 "I.cpp"
// #pragma GCC target("avx2,avx512f,avx512vl,avx512bw,avx512dq,avx512cd,avx512vbmi,avx512vbmi2,avx512vpopcntdq,avx512bitalg,bmi,bmi2,lzcnt,popcnt")
// #pragma GCC optimize("Ofast")

#line 2 "/home/sigma/comp/library/template.hpp"

#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using uint = unsigned int;
using ull = unsigned long long;
#define rep(i,n) for(int i=0;i<int(n);i++)
#define rep1(i,n) for(int i=1;i<=int(n);i++)
#define per(i,n) for(int i=int(n)-1;i>=0;i--)
#define per1(i,n) for(int i=int(n);i>0;i--)
#define all(c) c.begin(),c.end()
#define si(x) int(x.size())
#define pb push_back
#define eb emplace_back
#define fs first
#define sc second
template<class T> using V = vector<T>;
template<class T> using VV = vector<vector<T>>;
template<class T,class U> bool chmax(T& x, U y){
	if(x<y){ x=y; return true; }
	return false;
}
template<class T,class U> bool chmin(T& x, U y){
	if(y<x){ x=y; return true; }
	return false;
}
template<class T> void mkuni(V<T>& v){sort(all(v));v.erase(unique(all(v)),v.end());}
template<class T> int lwb(const V<T>& v, const T& a){return lower_bound(all(v),a) - v.begin();}
template<class T>
V<T> Vec(size_t a) {
    return V<T>(a);
}
template<class T, class... Ts>
auto Vec(size_t a, Ts... ts) {
  return V<decltype(Vec<T>(ts...))>(a, Vec<T>(ts...));
}
template<class S,class T> ostream& operator<<(ostream& o,const pair<S,T> &p){
	return o<<"("<<p.fs<<","<<p.sc<<")";
}
template<class T> ostream& operator<<(ostream& o,const vector<T> &vc){
	o<<"{";
	for(const T& v:vc) o<<v<<",";
	o<<"}";
	return o;
}
constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n-1); }

#ifdef LOCAL
#define show(x) cerr << "LINE" << __LINE__ << " : " << #x << " = " << (x) << endl
void dmpr(ostream& os){os<<endl;}
template<class T,class... Args>
void dmpr(ostream&os,const T&t,const Args&... args){
	os<<t<<" ~ ";
	dmpr(os,args...);
}
#define shows(...) cerr << "LINE" << __LINE__ << " : ";dmpr(cerr,##__VA_ARGS__)
#define dump(x) cerr << "LINE" << __LINE__ << " : " << #x << " = {";  \
	for(auto v: x) cerr << v << ","; cerr << "}" << endl;
#else
#define show(x) void(0)
#define dump(x) void(0)
#define shows(...) void(0)
#endif

template<class D> D divFloor(D a, D b){
	return a / b - (((a ^ b) < 0 && a % b != 0) ? 1 : 0);
}
template<class D> D divCeil(D a, D b) {
	return a / b + (((a ^ b) > 0 && a % b != 0) ? 1 : 0);
}
#line 5 "I.cpp"

struct segtree{
	using D = int;
	D inf = 1e9;

	int N;
	vector<D> val;

	segtree(){}
	segtree(int n){
		N=1;
		while(N<n) N*=2;
		val.assign(N*2,-inf);
	}
	segtree(const vector<D>& ds){
		int n = ds.size();
		N=1;
		while(N<n) N*=2;
		val.assign(N*2,-inf);
		rep(i,n) val[i+N] = ds[i];
		for(int i=N-1;i>0;i--) val[i] = max(val[i*2],val[i*2+1]);
	}
	void changemax(int k,D d){
		k+=N;
		if(val[k] >= d) return;
		val[k] = d;
		k/=2;
		while(k){
			val[k] = max(val[k*2],val[k*2+1]);
			k/=2;
		}
	}
	D getmax(int a,int b){
		D res = -inf;
		a+=N,b+=N;
		while(a<b){
			if(a&1) chmax(res,val[a++]);
			if(b&1) chmax(res,val[--b]);
			a/=2,b/=2;
		}
		return res;
	}
};


int main(){
	cin.tie(0);
	ios::sync_with_stdio(false);		//DON'T USE scanf/printf/puts !!
	cout << fixed << setprecision(20);
	using P = pair<int,int>;

	const int X = 1000000;
	int N,Q; cin >> N >> Q;
	V<int> A(N); rep(i,N) cin >> A[i];
	// int N = 150000, Q = 100000;
	// V<int> A(N,720720);
	VV<P> r2lqs(N);
	rep(q,Q){
		int l,r; cin >> l >> r; l--,r--;
		// int l = 0, r = N-1;
		r2lqs[r].eb(l,q);
	}


	VV<int> d2is(X+1);
	rep(i,N){
		int a = A[i];
		for(int x=1;x*x<=a;x++) if(a%x == 0){
			d2is[x].eb(i);
			if(x*x != a) d2is[a/x].eb(i);
		}
	}

	VV<P> k2ids(N);
	per1(d,X) if(si(d2is[d]) >= 3){
		auto& is = d2is[d];
		int K = si(is);
		rep(i,K-2){
			int j = i+1;
			int k = lwb(is,is[j]*2-is[i]);
			if(k != K){
				k2ids[is[k]].eb(is[i],d);
			}
		}
	}
	
	segtree seg(N);
	V<int> ans(Q);
	rep(r,N){
		// add k = r
		for(auto [i,d]: k2ids[r]){
			seg.changemax(i, d);
		}
		for(auto [l,q]: r2lqs[r]){
			ans[q] = seg.getmax(l,N);
		}
	}
	rep(q,Q) cout << ans[q] << '\n';
}