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 |
References
- McAdams, David E.. All Math Words Dictionary, least common multiple. 2nd Classroom edition 20150108-4799968. pg 107. Life is a Story Problem LLC. January 8, 2015. Buy the book
Cite this article as:
McAdams, David E. Least Common Multiple. 4/24/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/l/leastcommonmultiple.html.
Image Credits
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.)
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.)