Least Common Multiple
Pronunciation: /list ˈkɒm ən ˈmʌl tə pəl/ Explain
A least common multiple is the expression
of least degree or the least integer that is evenly divisible
by two or more expressions or integers. Take the integers 2 and 5.
The least integer that is evenly divisible by both 2 and 5 is 10. So
10 is the least common multiple of 2 and 5.
How to find a least common multiple
Example 1 - Find the least common multiple of 3 and 6
Step | Equation | Description |
1 | 3 = 3 | Find the prime factorization of the first integer. |
2 | 2·3 = 6 | Find all the prime factors of the second integer. |
3 | | Combine the prime factors of the two integers. |
Table 1: Least common multiple of 3 and 6. |
Example 2 - Find the least common multiple of 10 and 12
Step | Equation | Description |
1 | 10 = 2·5 | Find all the prime factors of the first integer. |
2 | 12 = 2^{2}·3 | Find all the prime factors of the second integer. |
3 | | Combine the prime factors of the two Multiples. |
Table 2: Least common multiple of 10 and 12. |
The least common multiples of the denominators are used when adding or subtracting fractions. In this case they are called
least common denominators.
Example 3: Find the least common multiple of x^{2} - x - 6 and x^{2} + 6x + 8
Step | Equation | Description |
1 | x^{2} - x - 6 = (x+2)(x-3) | Find all the prime factors of the first expression. |
2 | x^{2} + 6x + 8 = (x+2)(x+4) | Find all the prime factors of the second integer. |
3 | | Combine the prime factors of the two Multiples. |
Table 3: Least common multiple of x^{2} - x - 6 and x^{2} + 6x + 8 |
Cite this article as:
McAdams, David E. Least Common Multiple. 8/31/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/l/leastcommonmultiple.html.
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Revision History
8/31/2018: Removed broken links, updated license, implemented new markup. (
McAdams, David E.)
9/30/2010: Added graphics to improve readability. (
McAdams, David E.)
9/8/2010: Initial version. (
McAdams, David E.)