Write a function called smallest_multiple

2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder. Write a function called smallest_multiple that returns a uint64, the smallest positive number that is evenly divisible by all of the numbers from 1 to n where n is a positive integer scalar and is the only input argument of the function. If the result would be greater than what can be represented as a uint64, the function returns 0.

Answer 1

[Image Analyst]

Here is a hint:

function results = smallest_multiple(n)
    % Your code goes here

Next step, read this:

http://www.mathworks.com/matlabcentral/answers/8626-how-do-i-get-help-on-homework-questions-on-matlab-answers

Answer 2

[Srishti Saha]

Here is a solution that worked for me:

%%alternative solution to smallest multiple
function r = smallest_multiple(k) 
  r = uint64(1);
  for n = 1:k
      r = r * (n / gcd(r,n));   
  end
  if r == intmax('uint64')
     r = uint64(0);
  end
end

[Walter Roberson]

We discourage people giving complete answers for homework questions.

[Jan]

The question contains: "greater than what can be represented as a uint64". You test for equality only. This might seem to be a tiny difference, but it is very hard to catch "greater than intmax('uint64')" reliably.

[Walter Roberson]

The test is okay except for the case where the smallest multiple is exactly equal to intmax('uint64') which is 18446744073709551615 = 65537*(641*(17*(3*5)*257)*6700417) .

In any case where the result would be bigger than intmax('uint64') then the multiplications in the for loop would "saturate" at exactly intmax('uint64')

[Ranil Fernando]

My code is working outside the grader for n=13 without taking a longer time. But within the grader it fails for even 2. Someone please give me a hand here.

function multiN  = smallest_multiple(n)

mod2N = 0;
multiN = uint64(n);

while all(mod2N) == 0   

      multiN = multiN + 1;
      mod2N = zeros(1,n);

for ii=1:n
    if mod(multiN,ii) == 0
        mod2N(ii) = 1;  

      elseif multiN == intmax('uint64')
       multiN = uint64(0);

      end
  end

end