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The least common multiple, aka lowest common multiple of aka lowest common multiple of two integers a and b is the smallest positive integer that is divisible by both a and b.
The term is usually denoted lcm(a,b).
The easiest way to calculate the least common multiple of two or more integers is using our tool below.
Least Common Multiple Calculator
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Please note that our app is not limited to two integers;
it employs the associative law lcm(a,lcm(b,c)) = law lcm(lcm(a,b),c).
Likewise important, the lowest common multiple is commutative:
lcm(a,b) = lcm(b,a)
For the sake of completion,
lcm(b,b) = b; Idempotence
lcm(a,gcd(a,b)) = a; Absorption
What does the Least Common Multiple Mean?
Definition: For two given whole numbers a and b, the LCM is the smallest positive whole number that is divisible by both a and b.
Example of Least Common Multiple
For example, the lcm of 4 and 6, lcm(4,6) = 12.
Usage: For mathematical operations such as addition, subtraction and comparison with simple fractions, we often employ the lcm of the denominators usually referred to as lowest common denominator.
For example: 1/4 + 1/6 = 3/12 + 2/12 = 5/12.
How do You Find the Least Common Multiple?
Formula: you may use the greatest common factor (gcf) to determine the lcm of two numbers:
Alternatively, using prime factorization, the lcm is the product of multiplying the highest powers of each number expressed as prime number factorization.
Lcm(4,6) = 22 × 31 = 12.
Ahead is a chart with common values for your convenience.
Table
The aim of this table is to provide you with frequently searched lcms.
| Integer 1 | Integer 2 | LCM |
|---|---|---|
| 12 | 8 | 24 |
| 6 | 8 | 24 |
| 5 | 8 | 40 |
| 8 | 10 | 40 |
| 15 | 20 | 60 |
| 8 | 3 | 24 |
| 8 | 9 | 72 |
| 8 | 20 | 40 |
| 8 | 24 | 24 |
| 15 | 12 | 60 |
| 10 | 12 | 60 |
| 10 | 15 | 30 |
| 3 | 10 | 30 |
| 15 | 9 | 45 |
| 14 | 10 | 70 |
| 14 | 16 | 112 |
| 20 | 12 | 60 |
| 15 | 18 | 90 |
| 24 | 16 | 48 |
| 10 | 19 | 190 |
| 15 | 30 | 30 |
| 22 | 4 | 44 |
| 14 | 21 | 42 |
| 24 | 30 | 120 |
| 6 | 14 | 42 |
Next is the summary of our article.
Conclusion
Lcm(a,b) = the smallest positive integer that is divisible by both a and b.
This ends our article.
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– Article written by Mark, last updated on August 8th, 2023