Please carry out numbers be separate by a comma "," and click the "Calculate" button to find the LCM.

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330, 75, 450, 225 |

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### What is the Least common Multiple (LCM)?

In mathematics, the least common multiple, also known together the lowest usual multiple of 2 (or more) integers a and **b**, is the smallest confident integer the is divisible through both. The is typically denoted together LCM(a, b).

### Brute pressure Method

There room multiple ways to uncover a least typical multiple. The most an easy is merely using a "brute force" an approach that lists out each integer"s multiples.

EX: | Find LCM(18, 26)18: 18, 36, 54, 72, 90, 108, 126, 144, 162, 180, 198, 216, 23426: 52, 78, 104, 130, 156, 182, 208, 234 |

As deserve to be seen, this technique can be fairly tedious, and is far from ideal.

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### Prime administer Method

A more systematic way to uncover the LCM the some offered integers is to usage prime factorization. Element factorization requires breaking under each the the numbers being contrasted into its product of element numbers. The LCM is then identified by multiply the greatest power of each prime number together. Keep in mind that computer the LCM this way, while more efficient than using the "brute force" method, is still minimal to smaller sized numbers. Refer to the example listed below for clear up on exactly how to use prime administrate to identify the LCM:

EX: | Find LCM(21, 14, 38)21 = 3 × 714 = 2 × 738 = 2 × 19The LCM is therefore:3 × 7 × 2 × 19 = 798 |

### Greatest typical Divisor Method

A third viable an approach for recognize the LCM that some offered integers is using the greatest typical divisor. This is additionally frequently referred to as the greatest typical factor (GCF), among other names. Refer to the attach for details on how to recognize the greatest typical divisor. Offered LCM(a, b), the procedure because that finding the LCM making use of GCF is to divide the product of the number a and **b** by your GCF, i.e. (a × b)/GCF(a,b). Once trying to recognize the LCM of much more than 2 numbers, for example LCM(a, b, c) uncover the LCM the **a** and also **b** wherein the result will it is in **q**. Then find the LCM of **c** and **q**. The result will be the LCM of all three numbers. Utilizing the ahead example:

EX: | Find LCM(21, 14, 38)GCF(14, 38) = 2LCM(14, 38) = | 38 × 14 |

2 |

LCM(266, 21) = | 266 × 21 |

7 |

Note the it is not important which LCM is calculated an initial as long as every the numbers are used, and also the method is followed accurately. Relying on the details situation, each method has its own merits, and the user can decide which an approach to pursue at their own discretion.