# 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 and . 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
1 This is the expression to simplify.
2 Find all the prime factors of the first denominator.
3 Find all the prime factors of the second denominator.
4 Combine the prime factors of the two denominators.
5 What number times 10 equals the least common denominator?
6 What number times 12 equals the least common denominator?
7 Transform the first fraction.
8 Transform the second fraction.
9 Perform the addition.
Table 3: Adding 3/10 and 5/12.
1. McAdams, David E.. All Math Words Dictionary, least common denominator. 2nd Classroom edition 20150108-4799968. pg 107. Life is a Story Problem LLC. January 8, 2015. Buy the book
2. least common denominator. merriam-webster.com. Encyclopedia Britannica. Merriam-Webster. Last Accessed 8/31/2018. http://www.merriam-webster.com/dictionary/least common denominator. Buy the book
3. Carmichael, Robert D.. The Theory of Numbers. pp 3,12. www.archive.org. John Wiley & Sons. 1914. Last Accessed 8/31/2018. http://www.archive.org/stream/thetheoryofnumbe13693gut/13693-pdf#page/n17/mode/1up/search/common. Buy the book
4. Keigwin, H. W.. Principles of Elementary Algebra. pp 12-13. www.archive.org. Ginn & Company. 1886. Last Accessed 8/31/2018. http://www.archive.org/stream/principlesofelem00dupurich#page/12/mode/1up/search/common. Buy the book
5. Bettinger, Alvin K. and Englund, John A.. Algebra and Trigonometry. pg 31. www.archive.org. International Textbook Company. January 1963. Last Accessed 8/31/2018. http://www.archive.org/stream/algebraandtrigon033520mbp#page/n18/mode/1up. Buy the book

McAdams, David E. Least Common Denominator. 4/24/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/l/leastcommondenominator.html.

### Revision History

4/24/2019: Changed equations and expressions to new format. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)