What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 100?

Question

Following is my code where I tried to calculate LCM of all numbers from one to hundred by using BigInteger inn Java. But it does not provide any ans.

import java.math.BigInteger;

public class CommonOneToHundred {

    public static void main(String[] args) {
        // TODO Auto-generated method stub
        BigInteger res =new BigInteger("1");
        int i = 2;
        while(i<=100){
        res = lcm(res,BigInteger.valueOf(i));
        i++;
        }
        System.out.println(res);
    }
       static BigInteger lcm(BigInteger x, BigInteger y)
        {
            BigInteger a;
            //a = (x > y) ? x : y; // a is greater number
            a = y;
            while(true)
            {
                if(a.divide(x).equals(0) &&  a.divide(y).equals(0))
                    return a;
                a = a.add(BigInteger.ONE);
            }   
        }

}

advocateofnone · Answer 1 · 2016-09-10T15:40:00.247

5

Why not take multiplication of highest power's of all primes till 100. Here is my code in python.

primes = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97]
ans = 1
for prime in primes:
  power = 0
  tmp = 1
  while tmp <= 100:
    tmp = tmp*prime
    power += 1
  ans = ans * prime**(power-1)

print ans

The answer is 69720375229712477164533808935312303556800.

edited Sep 10 '16 at 15:40

answered Sep 10 '16 at 15:28

advocateofnone

2,527
3
17
39

can you please explain? – kulst Sep 10 '16 at 15:32
@kulst I added the code. Do comment if you have any doubts. – advocateofnone Sep 10 '16 at 15:36
1

@NikolasCharalambidis Nope, I can confirm that it is the correct result. – Tunaki Sep 10 '16 at 15:52
@NikolasCharalambidis Sure even I was doubtful that I made a mistake. Had to check again :D – advocateofnone Sep 10 '16 at 15:55
1

The trick is that your answer @Nikolas forgot to take into account the highest power of the prime, less than 100. The right power can actually be calculated: `log(100) / log(prime)`, no need to loop. – Tunaki Sep 10 '16 at 15:56
2

@sasha the ans is ryt. – kulst Sep 10 '16 at 16:04

Zhuoran He · Answer 2 · 2016-09-10T16:06:43.517

0

Using LCM accumulatively from 1 to 100 is going to take extremely long time, even if it does not overflow the BigInteger data type. Try a different algorithm. First prepare a prime table 2,3,5,7,...,97, then prime factorize every number from 1 to 100 and find the highest power of every prime in all 100 numbers. Finally, multiply those powers of prime factors using probably the BigInteger type. The answer is 2^6 * 3^4 * 5^2 * 7^2 * all primes from 11 to 97 = 69720375229712477164533808935312303556800. In fact, the prime factorization step can be saved. One can just find the highest power of each prime that is within 100 instead. The BigInteger multiplication cannot be avoided, since the number exceeds long long.

edited Sep 10 '16 at 16:06

answered Sep 10 '16 at 15:32

Zhuoran He

873
9
15

1

I prepared a prime table and multiplied all the prime no first. The ans is 2305567963945518424753102147331756070 for all prime. Then tried to take lcm(primefactor, allOtherNo), but it is very complicted. – kulst Sep 10 '16 at 15:36
According to my code the answer should be 69720375229712477164533808935312303556800, which is equal to 2^6 * 3^4 * 5^2 * 7^2 * all primes from 11 to 97. I checked with other softwares. It should be correct. – Zhuoran He Sep 10 '16 at 15:58

What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 100?

2 Answers2