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Least Common Multiple Calculator
Please offer numbers separated through a comma “,” and click on the “Calculate” button to locate the LCM.
https://www.lcm-calculator.com/
What is the Least Common Multiple (LCM)?
In mathematics, the least not unusualplace more than one, additionally referred to as the bottom not unusualplace more than one of (or extra) integers a and b, is the smallest high quality integer this is divisible through both. It is generally denoted as LCM(a, b).
Brute Force Method
There are more than one approaches to discover a least not unusualplace more than one. The maximum fundamental is definitely the usage of a “brute force” approach that lists out every integer’s multiples.
EX: Find LCM(18, 26)
18: 18, 36, 54, 72, 90, 108, 126, 144, 162, 180, 198, 216, 234
26: 52, 78, 104, 130, 156, 182, 208, 234
As may be seen, this approach may be pretty tedious, and is some distance from ideal.
Prime Factorization Method
A extra systematic manner to locate the LCM of a few given integers is to apply high factorization. Prime factorization entails breaking down every of the numbers being as compared into its made from high numbers. The LCM is then decided through multiplying the very best energy of every high range together. Note that computing the LCM this manner, whilst extra green than the usage of the “brute force” approach, remains restricted to smaller numbers. Refer to the instance under for rationalization on a way to use high factorization to decide the LCM:
EX: Find LCM(21, 14, 38)
21 = 3 × 7
14 = 2 × 7
38 = 2 × 19
The LCM is therefore:
3 × 7 × 2 × 19 = 798
Greatest Common Divisor Method
A 1/3 feasible approach for locating the LCM of a few given integers is the usage of the finest not unusualplace divisor. This is likewise regularly called the finest not unusualplace factor (GCF), amongst different names. Refer to the hyperlink for information on a way to decide the finest not unusualplace divisor. Given LCM(a, b), the technique for locating the LCM the usage of GCF is to divide the made from the numbers a and b through their GCF, i.e. (a × b)/GCF(a,b). When seeking to decide the LCM of extra than numbers, as an instance LCM(a, b, c) locate the LCM of a and b wherein the end result can be q. Then locate the LCM of c and q. The end result can be the LCM of all 3 numbers. Using the preceding example:
EX: Find LCM(21, 14, 38)
GCF(14, 38) = 2
LCM(14, 38) = 38 × 142 = 266
GCF(266, 21) = 7
LCM(266, 21) = 266 × 217 = 798
LCM(21, 14, 38) = 798
Note that it isn’t always vital which LCM is calculated first so long as all of the numbers are used, and the approach is observed accurately. Depending at the specific situation, every approach has its personal merits, and the consumer can determine which approach to pursue at their personal discretion.
