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Lcm of fractions

  1. Jun 7, 2008 #1
    how do i find lcm of two fractions ..say..

    2/3 and 5/8
    pls help
    Thank you
  2. jcsd
  3. Jun 7, 2008 #2


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    Hi endangered! :smile:

    The lcm of 3 and 8 is 2³.3, = 24.

    (So if you want 2/3 + 5/8, you write them as 16/24 + 15/24, = 31/24.)

    Note that fractions don't have an lcm, their denominators (their bottomy-bits) have an lcm! :smile:

    Generally, the lowest common multiple is found by splitting the two numbers nto their prime factors, and taking the larger power of each.

    So for example, what is the lcm of 24 and 90?

    Well, 24 = 2³.3, and 90 = 2.3².5, so the lcm is 2³.3².5, = 360. :smile:
  4. Jun 7, 2008 #3
    are you sure???

    cause this is a assignment from my math sir..to find lcm of--repeat--FRACTIONS..
  5. Jun 7, 2008 #4

    matt grime

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    Perhaps you could say what your teacher defined the lcm of two fractions as?

    We can guess, but it's better if we don't have to.
  6. Jun 7, 2008 #5


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    The least common denominator of fractions is the least common multiple of their denominators. Your teacher may be using the two terms intechangeably. It's "loose" terminology but as long as you are only talking about fractions, not a problem.
  7. Jun 9, 2008 #6
    I am quite sure that he is not using the terms interchangebly..but if you are sure that lcm of two fractions does not exist..then i could tell him..

    but this online lcm calculator returns the value of lcm of 2.3 and 3.5 as "8.0499"..

    what do you have to say about that?how is it returning this definite value,if lcm of fractions does not exist?
  8. Jun 9, 2008 #7


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    Because 2.3 times 3.5 is 8.05 !!! :smile:

    Any multiple of 8.05 is also a multiple of both 2.3 and 3.5 ! :smile:

    Any multiple of any two numbers is a multiple of their product, and so in that sense, their product is their lcm!

    And your calculator knows that! :wink:
  9. Jun 9, 2008 #8

    D H

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    The term "least common multiple" applies to integers. Take your example of 2.3 and 3.5, whose product is 8.05. Well, isn't 0.805 is also a multiple of both 2.3 and 3.5? Even pi is a multiple (non-rational multiple) of 2.3. So, as we have said, it is best if you explained your instructor's terminology.
  10. Jun 10, 2008 #9


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    As already pointed out LCM is usually reserved for integers, but I suppose it could be generalized to fractions in a sensible way.

    First off it must be clear that simply changing all references in the definition from integers to fractions will NOT make any sense. That is, if you try the definition: "the LCM of two fractions is the smallest positive fraction that is a fractional multiple of both original fractions" then it's easy to show that this is meaningless (as no such fraction exists).

    The following definition does at least make sense (and I'd assume it to be the most logical way to define the LCM of fractions if we must do so). Proposed definition: "The LCM of two fractions is the smallest positive fraction that is an integer multiple of both original fractions".

    Personally I've never seen the term LCM applied to fractions like this, but the above definition does seem a reasonable one. Scratching around just now with that particular definition I came up with the following interesting result:

    If f1 = num1/den1 and f2 = num2/den2 are both fractions in their simplest form, then LCM(f1,f2) = LCM(num1.num2)/GCD(den1,den2).

    BTW. Can anyone confirm the above result?
  11. Nov 7, 2010 #10
    Sorry to drag up an old thread but;
    I need to find LCM of a list of fractions.
    They're actually decimals, horrible decimals so it's much easier to display as fractions.

    please note this is not an instructor/teacher set problem but a real world problem I need solving.

    I have 9 incremental series, each starting at 0 and increasing by a different figure.
    I need to find the smallest figure that appears in each list.
    the increments are

    listed as fractions

    any suggestions?
    cheers muchly
  12. Nov 7, 2010 #11


    Staff: Mentor

    The LCM of the denominators of the nine fractions you showed is the smallest number that is evenly divisible by all nine denominators.

    Here is a list of the denominators and their factors. (Note that there are only eight, since one denominator appears twice.)
    25 = 5*5
    20 = 2*2*5
    16 = 2*2*2*2
    14 = 2*7
    12 = 2*2*3
    120 = 2*2*2*3*5
    9 = 3*3
    15 = 3*5

    The LCM of these numbers will need to have as many 2's as appear the most times above, as many 3's as appear the most times above, as many 5's as appear the most times above, and as many 7's as appear the most times above.

    This means there will need to be
    -four factors of 2 (because 16 contains this many factors of 2)
    -two factors of 3 (because 9 contains this many factors of 3)
    -two factors of 5 (because 25 contains this many factors of 5)
    -one factor of 7 (because 14 contains this many factors of 7)

    So the LCM is 2*2*2*2*3*3*5*5*7 = 25,200
  13. Feb 27, 2011 #12
    the correct ans iso:)
    lcm of the numerators divded by the hcf of the denominators:!!)
  14. Feb 27, 2011 #13
    Hehe I see where the guy got confused on this one. Tiny was right but was showing stuff like 2.3 and 5.7 when what he meant was 2*3 and 5*7. So the guy was thinking he meant 2point3 and 5point7 ect. Is it common for people to right 2.3 instead of 2*3 outside of the us or something?
  15. Feb 27, 2011 #14


    Staff: Mentor

    It's very confusing if they write 2.3 when they mean [itex]2 \cdot 3[/itex], which is often used in math textbooks. Because it's a hassle to get that dot raised up (there's no key on a keyboard that can do it), people often use the symbol for multiplication that is used universally in programming - *.
  16. May 28, 2012 #15
    Write the fractions using a common denominator, then find the LCM of the numerators. Divide that by the common denominator and reduce the result.

    2/3 = 16/24
    5/8 = 15/24
    LCM(16, 15) = 16*15 = 240

    LCM of 2/3, 5/8 is 240/24 = 10
    10 = 15*2/3 = 16*5/8
  17. May 28, 2012 #16
    Your list of fractions can be expressed over the common denominator 25,200. When they are, the LCM of their numerators is 1,663,200. The ratio of these numbers is the LCM of your fractions. It is 66.
    Last edited: May 28, 2012
  18. May 29, 2012 #17
    I just want to point out that this thread will be 4 years old in a few days. Perhaps we should plan a party.

    I also think that the consensus is that fractions do not have LCMs.

    Perhaps we should lock this so it doesn't creep up to the front page next year.
  19. May 29, 2012 #18
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