Least Common Denominator

Pronunciation: /list ˈkɒm ən dɪˈnɒ məˌneɪ tər/ Explain

A least common denominator is the least common multiple of two or more denominators. Take the fractions 1/3 and 1/6. The smallest number that evenly divided by both 3 and 6 is 6. So 6 is the least common denominator of 3 and 6 is 6.

Example 1
StepEquationDescription
13Find all the prime factors of the first denominator.
22·3Find all the prime factors of the second denominator.
32·3 = 6Combine the prime factors of the two denominators.
Table 1: Least common denominator of 3 and 6.

Least common denominators are used when adding or subtracting fractions. Since two fractions can be added or subtracted only if they have the same denominator, the least common denominator is used to transform the fractions.

Example 3
StepEquationDescription
13/10+5/12This is the expression to simplify.
210=2*5Find all the prime factors of the first denominator.
312=2^2*3Find all the prime factors of the second denominator.
42^2*3*5=60Combine the prime factors of the two denominators.
56*10=60What number times 10 equals the least common denominator?
65*12=60What number times 12 equals the least common denominator?
76*2/(6*10)=12/60Transform the first fraction.
85*5/(5/12)=25/60Transform the second fraction.
912/60+25/60=(12+25)/60=37/60Perform the addition.
Table 3: Adding 3/10 and 5/12.

References

  1. least common denominator. merriam-webster.com. Encyclopedia Britannica. Merriam-Webster. Last Accessed 8/30/2018. http://www.merriam-webster.com/dictionary/least common denominator.
  2. Carmichael, Robert D.. The Theory of Numbers. pp 3,12. www.archive.org. John Wiley & Sons. 1914. Last Accessed 8/30/2018. http://www.archive.org/stream/thetheoryofnumbe13693gut/13693-pdf#page/n17/mode/1up/search/common. Buy the book
  3. Keigwin, H. W.. Principles of Elementary Algebra. pp 12-13. www.archive.org. Ginn & Company. 1886. Last Accessed 8/30/2018. http://www.archive.org/stream/principlesofelem00dupurich#page/12/mode/1up/search/common. Buy the book
  4. Bettinger, Alvin K. and Englund, John A.. Algebra and Trigonometry. pg 31. www.archive.org. International Textbook Company. January 1963. Last Accessed 8/30/2018. http://www.archive.org/stream/algebraandtrigon033520mbp#page/n18/mode/1up. Buy the book

Cite this article as:

McAdams, David E. Least Common Denominator. 8/31/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/l/leastcommondenominator.html.

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Revision History

8/31/2018: Removed broken links, updated license, implemented new markup. (McAdams, David E.)
9/16/2008: Initial version. (McAdams, David E.)

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