# Equalizing fractions

When I was in grade 3, we were taught how to solve a very simple math problem. It was equaling the denominators of two or more fractions.

Let's take two proper fractions:-

$$\frac{1}{2},\frac{2}{3}$$

First we will take the Least Common Multiple of the denominators of the two fractions, the LCM of $$\2,3\$$ are $$\6\$$. Then we divide the LCM ($$\6\$$) by the denominators of both fractions ($$\6\$$) and we get $$\3,2\$$ and serially multiply them with the numerators of the both fractions and get

$$\frac{3}{6},\frac{4}{6}$$

And that's the result.

# Challenge

Take two or more fractions, and equalize their denominators.

# I/O format

You can take an array/list of (numerator,denominator) pairs. Pre-defining them in TIO header is allowed. You can take in other better ways too.

Input: ((1,2),(2,3)) or
1,2 2,3
1/2 2/3
Output: (3,6),(4,6) or
3,6 4,6
3/6 4/6
Input:  ((1, 8), (5, 12))
1,8 5,12
1/8 5/12
Output: ((3, 24), (10, 24))
3,24 10,24
3/24 10/24
Input: ((1, 2),(2, 3),(4, 6))
Output: 3/6 4/6 4/6


# Rules

• Standard loopholes are forbidden. (except use of TIO headers to pre-define input)
• Trailing whitespace in output is allowed.
• Please explain your answer. This is not necessary, but it makes it easier for others to understand.
• Languages newer than the question are allowed. This means you could create your own language where it would be trivial to do this, but don't expect any upvotes.
• This is , so shortest code in bytes wins!
• Sorry to bother again, but if non-simplified fractions can appear in the input (as it looks like from the last testcase), you may consider adding a testcase like 2/4, 3/6, where computing the LCM of the denominators is not enough. Apr 1 at 10:15
• @Wasif You posted in the sandbox yesterday. Then you post today complaining that it might be treated as if you didn't post to the sandbox at all! T_T Wait a few days for feedback from the sandbox posting and then you won't be in such dilemma. Apr 1 at 12:01
• I'm voting to close as unclear because it's not apparent to me from the challenge how non-reduced fractions are handled.
– xnor
Apr 1 at 14:15
• You have many choices to clarity the question: 1. Change the rule to: Inputs will never contain non-reduced fractions (or input with non-reduced factions may lead to undefined behaviors), change last testcase to avoid it; 2. Clarity that input may contain non-reduced fractions, and answers should always use LCM of denominator, add a testcase (2/4, 3/6) -> (6/12, 6/12); 3. Clarity that input may contain no-reduced factions, and answers should not use LCM of denominator, but the smallest possible value, add a testcase (2/4, 3/6) -> (1/2, 1/2);
– tsh
Apr 2 at 1:41
• Also, you need to add your comment to "Are all numbers in the input positive integers" into the question. Not only leave it in comment.
– tsh
Apr 2 at 1:42

# JavaScript (Node.js), 63 bytes

f=(a,t=1)=>a.some(v=>t%v[1])?f(a,1+t):a.map(([p,q])=>[p*t/q,t])


Try it online!

# JavaScript (Node.js), 63 bytes

f=(a,t,b=a.map(([p,q])=>[m=p*t/q,o&=m%1||t],o=t))=>o?b:f(a,-~t)


Try it online!

m=p*t/q cannot be changed to p*=t/q due to floating point errors. For example, 11*15/11 is 15, but 11*(15/11) is 14.999999999999998. :(

• The first answer here will output [[6, 12], [6, 12]] for input [[2, 4], [3, 6]].
• The second one will output [[1, 2], [1, 2]] for input [[2, 4], [3, 6]].

# JavaScript (Node.js), 62 bytes

• @Arnauld had modified the code to make it work in 62 bytes. This one would support positive fractions.
f=(a,t,o=-~t,b=a.map(([p,q])=>[p*t/q,t+=p*t%q]))=>t<o?b:f(a,o)


Try it online!

# Wolfram Language (Mathematica), 20 bytes

LCM@@(q=Last/@#)/q#&


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Fractions are in the form {numerator, denominator}
We simply multiply the fractions by the LCM of denominators divided by the denominators

# Factor, 73 64 bytes

-9 bytes thanks to chunes!

[ dup 1 [ lcm ] reduce [ swap n/v v* dup length ] keep <array> ]


Try it online!

Takes the input as two separate lists for numerators and denominators

# Factor, 73 bytes

[ unzip dup 1 [ lcm ] reduce swap over [ n/v v* ] dip '[ _ 2array ] map ]


Try it online!

Takes the input as a list of (numerator,denominator) pairs.

I thought it would be shorter using fractions but I didn't manage to make it nice. Except this the Factor version TIO has normalizes the fractions.

• We came up with similar answers, but I took the input as two separate lists for numerators and denominators. Apr 1 at 12:27
• @chunes Thanks for sharing! Feel free to post it as a separate submission. Apr 1 at 12:31
• @chunes I updated the post using your solution - tahnks again! Apr 2 at 6:29

# J, 14 10 bytes

,.**./@]%]


Try it online!

-4 after realizing taking a list of numerators and a list of denominators was allowed

Works like <list of numerators> f <list of denominators>.

• *./@] LCM of denominators (right hand arg)...
• %] Divided elementwise by the denominators...
• ,.* Times the zip of the numerators and denominators.

# Ruby, 57 bytes

->l{k=l.reduce(1){|s,x|s.lcm x[1]};l.map{|a,b|[a*k/b,k]}}


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# Jelly, 9 8 bytes

aæl/Ṅ:Ʋ×


Try it online!

Full program. Takes a list of denominators $$\[d_1, d_2, ...]\$$ on the left and a list of numerators $$\[n_1, n_2, ...]\$$ on the right. Outputs a list of denominators, then a list of numerators

Would be 7 bytes if we could just output the dominator once.

## How it works

aæl/Ṅ:Ʋ× - Main link. Takes denominators D on the left and numerators N on the right
Ʋ  - Group the previous 4 links into a monad on D:
æl/     -   Reduce by LCM
a        -   AND; Replace each element in D with the LCM
Ṅ    -   Print the list of LCM
:   -   Divide each by the corresponding element of D
× - Multiply this list with N elementwise


n#d=($d).zipWith(div.(*foldr1 lcm d))<$>[n,d]


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Takes two lists (n=numerators and d=denominators) as input, returns two lists with the same format as output. Assumes fractions in the input are reduced.

f x|l<-foldr(\(n,d)->lcm.div d$gcd n d)1x=[(div(n*l)d,l)|(n,d)<-x]  Try it online! Takes a list of pairs as input, returns a list of pairs as output. Works for unreduced fractions as well. # Haskell, 79 bytes f x|let(z,l)=foldr(\(n,d)(y,a)->((div(n*l)d,l):y,lcm(ddivgcd n d)a))([],1)x=z  Takes a list of pairs as input, returns a list of pairs as output. Works for unreduced fractions as well. Quite a bit longer than the other answer, but I decided to post it anyway since there is some Haskell magic going on! The LCM of the (reduced) denominators l appears both on the left hand side and the right hand side of the let expression. This is only possible because of Haskell's lazyness. # Pyth, 33 bytes K1JEFkJ=K/*kKikK;FkE[/*kKhJK)=JtJ  Try it online! Takes two lines of input: first line should contain the list of denominators, and the second line should contain the list of corresponding numerators. # Explanation K1 # Initialize K to 1 JE # Initialize J to evaluated input (in this case, list of denominators) FkJ # For loop over elements of J, with iterator as k =K # Set K to *kK # Product of k and K ikK # GCD of k and K / # Divide them to get the LCM FkE # Another for loop over the next evaluated input (the numerators) hJ # First element of J /*kKhJ # Convert the numerator accordingly K # Denominator [...) # Put that inside a list and print it tJ # Tail J (first element removed) =J # Assign J to it  # Python 3, 99 bytes import numpy f=lambda a,i=0,k=1:i<len(a)and f(a,i+1,numpy.lcm(k,a[i][1]))or[(p*k//q,k)for p,q in a]  Try it online! Takes a list of lists and computes the LCM of denominators. This result is stored in k and at the end the fractions are converted to the same denominator (k). # Retina, 82 bytes \d+ * +(_+)/((_+)(\3)*) (_+)/(?!\2\b)(\3)+\b$#6*$1/$#6*$2$#4*$5$5/$#6*$2
_+
$.&  Try it online! Link includes test cases. Explanation: \d+ *  Convert to unary. +  Repeat until all denominators are equal. (_+)  Match a numerator... /((_+)(\3)*)  ... and the largest factor of a denominator...  (_+)  ... and another numerator... /(?!\2\b)(\3)+\b  ... and a denominator that is not equal to the first denominator but with the shared (greatest) common divisor. $#6*$1/$#6*$2$#4*$5$5/$#6*$2


Multiply the first fraction by the multiplicity $#6 of the GCD in the second fraction, and also update the second fraction. _+$.&


Convert to decimal.

# Charcoal, 30 bytes

≔Ｅθ⊟ιη≔¹ζＷ⌈﹪ζη≦⊕ζＩＥθ⟦÷×ζ⊟ι§ηκζ


Try it online! Link is to verbose version of code. I/O is standard Charcoal array format. Explanation: Uses brute force.

≔Ｅθ⊟ιη


Get the denominators.

≔¹ζ


Assume the LCM is 1.

Ｗ⌈﹪ζη≦⊕ζ


Keep incrementing the LCM until all the denominators divide it.

ＩＥθ⟦÷×ζ⊟ι§ηκζ


Scale the fractions to the new denominator.

# R, 69 66 bytes

Edit: -3 bytes thanks to Giuseppe

function(m)m/m[,2]*which(!rowSums(outer(1:prod(m),m[,2],"%%")))[1]


Try it online!

Input & output as 2-column matrices, with each row representing a pair of numerator & denominator.

• 66 bytes Apr 6 at 21:07
• @Giuseppe - Thanks. Nice exploitation of which bringing the elements into-order to avoid the need for min. I like it. Apr 8 at 17:53

# Excel, 130 bytes

=LET(n,COUNT(A:A),b,OFFSET(B1,,,n),q,SEQUENCE(PRODUCT(b)),MIN(IF(MMULT(1*(MOD(q,TRANSPOSE(b))=0),b^0)=n,q,""))/b*OFFSET(A1,,,n,2))


Uses columns A&B for input

=LET(
n,COUNT(A:A)                                                            ' Number of fractions
b,OFFSET(B1,,,n)                                                        ' List of denominators
q,SEQUENCE(PRODUCT(b))                                                  ' 1..product of all denominators
MIN(IF(MMULT(1*(MOD(q,TRANSPOSE(b))=0),b^0)=n,q,""))/b*OFFSET(A1,,,n,2) ' final calculation
1*(MOD(q,TRANSPOSE(b))=0)                                  ' matrix of q by b where 1 indicates q mod b = 0
IF(MMULT(                         ,b^0)=n,q,"")                     ' if q is divisible by all n numbers then q else "" (list of all common multiples)
MIN(                                               )                    ' least common multiple
/b*OFFSET(A1,,,n,2) ' multiply each row by the number need to change denominator to LCM


# 05AB1E, 9 bytes

.¿©¹÷*®δ‚


Input as two separated lists, first the list of denominator, second the list of numerator.
Output as a list of pairs of [numerator, denominator].

Explanation:

.¿         # Get the Least Common Multiple (LCM) of the first (implicit) input-list of
# denominators
©        # Store this value in variable ® (without popping)
¹÷      # Integer-divide it by each value of the first input-list
*     # Multiply each value at the same positions to the second (implicit)
# input-list of numerators
δ   # For each value:
® ‚  #  Pair it with the stored LCM of variable ®
# (after which the resulting list of pairs is output implicitly as result)


# Julia, 22 bytes

n$d=(l=lcm(d))n./d.=>l  Try it online! • expects [numerators]$ [denominators]
• outputs an array of pairs : [num1 => den1, num2 => den2,...]
• could be 20 bytes with the denominator only once in the ouput