Difference between revisions of "Least common multiple"
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| − | The "least common multiple" (LCM) of two or more numbers is the lowest multiple common to both. Any set of numbers have an infinite amount of common [[multiples]] but only one LCM. | + | The "least common multiple" (LCM) of two or more numbers is the lowest multiple common to both. Any set of numbers have an infinite amount of common [[multiples]], but only one LCM. |
== How to find == | == How to find == | ||
| − | The most primitive way to find the LCM of a set of numbers is to list out the multiples of each until you find a multiple that is common to all of them. This is a tedious method, so it is usually only used when the numbers are small. For example, suppose we wanted to find the LCM of two numbers 4 and 6. We would begin by listing the multiples of 4 and 6 until we find the smallest number in both lists, as shown below. | + | The most primitive way to find the LCM of a set of numbers is to list out the multiples of each until you find a multiple that is common to all of them. This is a tedious method, so it is usually only used when the numbers are small. For example, suppose we wanted to find the LCM of two numbers, 4 and 6. We would begin by listing the multiples of 4 and 6 until we find the smallest number in both lists, as shown below. |
4 8 '''12''' | 4 8 '''12''' | ||
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12 is the LCM of 4 and 6. | 12 is the LCM of 4 and 6. | ||
| − | The LCM of two numbers can be found more easily by first finding the [[Greatest_common_divisor | greatest common divisor (GCD)]]. Once the GCD is known the LCM is calculated by the following equation, <math> LCM(a, b) = \frac{a \times b}{GCD(a, b)} </math>. | + | The LCM of two numbers can be found more easily by first finding the [[Greatest_common_divisor | greatest common divisor (GCD)]]. Once the GCD is known, the LCM is calculated by the following equation, <math> LCM(a, b) = \frac{a \times b}{GCD(a, b)} </math>. |
Let's use the above example again. The GCD of 4 and 6 is 2, since <math> 4 = 2^2 </math> and <math> 6 = 2 \times 3</math>. Using the above equation, we find <math> LCM(4, 6) = \frac{4 \times 6}{2} = \frac{24}{2} = 12 </math>. | Let's use the above example again. The GCD of 4 and 6 is 2, since <math> 4 = 2^2 </math> and <math> 6 = 2 \times 3</math>. Using the above equation, we find <math> LCM(4, 6) = \frac{4 \times 6}{2} = \frac{24}{2} = 12 </math>. | ||
Revision as of 13:02, 20 June 2006
The "least common multiple" (LCM) of two or more numbers is the lowest multiple common to both. Any set of numbers have an infinite amount of common multiples, but only one LCM.
How to find
The most primitive way to find the LCM of a set of numbers is to list out the multiples of each until you find a multiple that is common to all of them. This is a tedious method, so it is usually only used when the numbers are small. For example, suppose we wanted to find the LCM of two numbers, 4 and 6. We would begin by listing the multiples of 4 and 6 until we find the smallest number in both lists, as shown below.
4 8 12
6 12
12 is the LCM of 4 and 6.
The LCM of two numbers can be found more easily by first finding the greatest common divisor (GCD). Once the GCD is known, the LCM is calculated by the following equation, 
.
Let's use the above example again. The GCD of 4 and 6 is 2, since 
and 
. Using the above equation, we find 
.
