How to get the Least common multiple of a fractional number

Question

Tristan 2013-11-13

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回答： Martin Grden 2024-3-1

在 MATLAB Online 中打开

for example:

>> lcm(8,20)

ans =

40

works

>> lcm(1.6,1)

doesn't work :(

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Tristan 2013-11-13

I should be getting 8

Image Analyst 2013-11-13

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

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Answer 1

Walter Roberson 2013-11-13

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在 MATLAB Online 中打开

rat(1/1.6)

and take the denominator term.

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Answer 2

Kaixiang Wang 2015-8-23

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在 MATLAB Online 中打开

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

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Xiangming Hao 2017-5-17

It works, thank you!

Walter Roberson 2017-5-17

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()

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Answer 3

John D'Errico 2013-11-13

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编辑：John D'Errico 2013-11-13

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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.

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Answer 4

Martin Grden 2024-3-1

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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