How to get the Least common multiple of a fractional number

for example:

>> lcm(8,20)

ans =

    40

works

>> lcm(1.6,1)

doesn't work :(

[Tristan]

I should be getting 8

[Image Analyst]

http://matlab.wikia.com/wiki/FAQ#Why_is_0.3_-_0.2_-_0.1_.28or_similar.29_not_equal_to_zero.3F

Answer 1

[Walter Roberson]

rat(1/1.6)

and take the denominator term.

Answer 2

[Kaixiang Wang]

Inspired by one of the comments, actually you could do this with Symbolic toolbox.

x=sym(1.6);
y=sym(1);
lcm(x,y) % should give you the answer you want

[Xiangming Hao]

It works, thank you!

[Walter Roberson]

Yes, sym() of a double precision value by default tries to represent the value as a rational value, looking for a good approximation -- for example it is able to figure out pi/2 as a multiple of sym('pi') . And once you have rational form then you can proceed towards lcm()

Answer 3

[John D'Errico]

Actually, no, you cannot get that result.

The real problem is that MATLAB does not actually represent 1.6 as 1.6. Using my HPF tool, we find that 1.6 is actually stored as

hpf(1.6,60)
ans =
1.60000000000000008881784197001252323389053344726562500000000

Yep. Not exactly 1.6. Floating point storage in a binary form prevents storing most decimal numbers exactly.

In turn, this means that any algorithm that yields a LCM that works on integers will fail when looking for exact multiples of real numbers.

Answer 4

[Martin Grden]

A solution for more than two numbers. You need to split the fractions into two input vectors.

function result=lcm_e(numeratorVector,denominatorVector)
% horiz. vector args req.

z=denominatorVector;

if length(z)==2
    lcmDenominatorVector=lcm(z(1),z(2));
else
    lcmDenominatorVector=lcm(z(1), ilcm_e(z(2:end)));
end

z=(lcmDenominatorVector./denominatorVector).*numeratorVector;

if length(z)==2
    lcmNumeratorVector=lcm(z(1),z(2));
else
    lcmNumeratorVector=lcm(z(1), ilcm_e(z(2:end)));
end

result=lcmNumeratorVector/gcd(lcmNumeratorVector,lcmDenominatorVector);

  function ierg=ilcm_e(z)
        if length(z)==2
            ierg=lcm(z(1),z(2));
        else
            ierg=lcm(z(1),ilcm_e(z(2:end)));
        end
  end

end