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Lesson 2: Common denominators

# Finding common denominators

Learn all about finding common denominators in fractions. Watch how to use the least common multiple of the denominators to rewrite fractions, making them easier to compare or add. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• How do I find LCM with 3 fractions
• Its quite simple you find out what the three numbers are, lets say the numbers are: 2,3,4.
then you wright the numbers they all have in common.
2: 2,4,6,8,10,12
3: 3,6,9,12
4: 4,8,12
Then circle or look to find witch they all have In common. If you look hard they all have or are equal to the number 12. I hope my answer helped you answer your question :)
• What if one of the denominators is a 1?
• If the denominator is a 1, then it's still the same formula: you simply divide the denominator by the numerator (ex: 4/1 = 4 divided by 1 = 4). It works no matter what the numerator or denominators are, even if the denominator isn't a 1 (ex: 7/3 = 7 divided by 3 = 2 1/3). With 4/1, it's easy to know that it will be 4, but with bigger numbers (ex: 282/47), it can be a lot harder to mentally figure out what your answer will be, so the dividing trick can help a lot in those scenarios. I know this answer is really late -- four years late; sorry -- but I hope either you see this, Noah, or somebody else who needed help sees this and gets the help that they need. :)
• how is 2/8 the same as 6/24 and 5/6 the same as 20/24
• Well, 2/8 is equivalent to 6/24 because the ratio is the same. The ratio is 1/4, and any same-numerator-denominator pair that's multiplied with it just changes the numerator and denominator. The hard-boiled value of the fraction is the same: 1/4.

It's a little hard to visualize, but here:
1/4 times 2/2 is what? 2/8.
2/8 times 3/3 is what? 6/24.
6/24 times 4/4 is what? 24/96.
24/96 divided by 24/24? 1/4!

So long as you continue to multiply the fraction by ONLY same-numerator-denominator fractions the ratio and value will stay the same, and thus the fractions will equal each other.

Tip: This means that you can simplify larger fractions down using a numerator-denominator to its smallest form. Keep in mind, though, that it helps to find the common factor(preferably greatest) of both the numerator and denominator before creating your same-numerator-denominator pair.

For example: 100/120 + 43 (Don't mind the +43, this is solely to simplify the fraction 100/240)

100 and 120 are both divisible by these numbers: 1, 2, 4, 5, 10, and 20. To simplify the fraction, you just need to divide the fraction by a same-numerator-denominator pair like this:
100/120 / 20/20 = 5/24
Thus, the "true" and simplified value of 100/240 is 5/24.

I know this was really winded, but I hope it helps. Let me know if you need help on anything else!
• How do I find the LCD of two rational equations? If there is a video for this can you point me to it?
• I have a question. How do you find the least common denominator by using the prime factorization method?
(1 vote)
• Maybe an example would answer your question. There are three denominators, 6, 8, and 9 and you want the least common denominator. 6=3*2, 8=2*2*2, and 9=3*3. Start with any of the numbers, 3*2. If the next has any in common, eliminate it, so one 2 is eliminated giving 3*2*2*2. The next has one 3 in common, so eliminate one 3, final LCM is 3*2*2*2*3. Try 10, 18, and 24. 10=5*2, 18=3*3*2, 24=3*2*2*2. So you start with 5*2, one two in common with 18, so eliminate it to get 5*2*3*3, last (24) has both a 3 and 2 in common now that you can eliminate, so 5*2*3*3*2*2=360. Hope this makes sense.
• Can someone explane this to me pls?
• So you have to find a common denominator, right? For this one, you have to multiply to get the common denominator. So what times 6 equals 24? Also, what times 8 equals 24? Then that is how you get your common denominator.
• is LCM n LCD are same?
• The LCM is used to find the LCD but yes they are the same
• What's a common denominator?
• A common denominator is a denominator that you can reach by both denominators. For example in the problem 3/4+ 5/6 a common denominator is 12 because it is the lowest number that both 4 and 6 can reach by multiplying with whole numbers. Thanks for reading hope it helps!
• How to know if you are finding the common denominators with some choices like; 3/4+1/3

A.3/4+1/3 = 9/12+4/12

B.3/4+1/3=9/12+3/12

C.3/4+1/3=12/12+4/12

D.3/4+1/3=3/12+1/12