Lcm of fractions

Hi endangered!

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!

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.

 

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.

 

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.

 

Because 2.3 times 3.5 is 8.05 !!!

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

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!

 

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.

 

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?

 

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
0.04
0.05
0.0625
0.071428571
0.083333333
0.091666667
0.111111111
0.133333333
0.15

listed as fractions
1/25
1/20
1/16
1/14
1/12
11/120
1/9
2/15
3/20

any suggestions?
cheers muchly

 

the correct ans is
lcm of the numerators divded by the hcf of the denominators:!!)

 

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?

 

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

 

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.

 

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.

 

Agreed!