# Calculate the Least (the Lowest) Common Multiple of Numbers, LCM, Using Two Methods: Either the Prime Factorization of Numbers, the Numbers' Divisibility, or the Euclidean Algorithm. Online Calculator

## Calculator: calculate the least common multiple, lcm

### Calculate the least common multiple of the numbers, LCM:

#### Method 1: Run the prime factorization of the numbers - then multiply all the prime factors of the numbers, taken by the largest exponents.

#### Method 2: The Euclidean algorithm:

lcm (a; b) = ^{(a × b)} / _{gcf (a; b) }

#### Method 3: The divisibility of the numbers.

## The least (the lowest) common multiple, LCM: the latest 10 calculated values

** What is the least (the lowest) common multiple, LCM, of the numbers 299 and 2,091 and how to calculate it? ** | *Sep 22 09:38 UTC (GMT)* |

** What is the least (the lowest) common multiple, LCM, of the numbers 2,829 and 458 and how to calculate it? ** | *Sep 22 09:38 UTC (GMT)* |

** What is the least (the lowest) common multiple, LCM, of the numbers 1,018 and 311 and how to calculate it? ** | *Sep 22 09:38 UTC (GMT)* |

** What is the least (the lowest) common multiple, LCM, of the numbers 4,168 and 31 and how to calculate it? ** | *Sep 22 09:38 UTC (GMT)* |

** What is the least (the lowest) common multiple, LCM, of the numbers 106 and 1,025 and how to calculate it? ** | *Sep 22 09:38 UTC (GMT)* |

** What is the least (the lowest) common multiple, LCM, of the numbers 1,645 and 8,269 and how to calculate it? ** | *Sep 22 09:38 UTC (GMT)* |

** What is the least (the lowest) common multiple, LCM, of the numbers 2,339 and 52 and how to calculate it? ** | *Sep 22 09:38 UTC (GMT)* |

** What is the least (the lowest) common multiple, LCM, of the numbers 999,999,999,916 and 1,256 and how to calculate it? ** | *Sep 22 09:38 UTC (GMT)* |

** What is the least (the lowest) common multiple, LCM, of the numbers 5,509 and 871 and how to calculate it? ** | *Sep 22 09:38 UTC (GMT)* |

** What is the least (the lowest) common multiple, LCM, of the numbers 19,845 and 138,958 and how to calculate it? ** | *Sep 22 09:38 UTC (GMT)* |

** The least (the lowest) common multiple, LCM: the list of all the operations ** |

## The least common multiple (lcm). What it is and how to calculate it.

- The number 60 is a common multiple of the numbers 6 and 15 because 60 is a multiple of 6 (60 = 6 × 10) and also a multiple of 15 (60 = 15 × 4).
**There are infinitely many common multiples of 6 and 15. **

**If the number "v" is a multiple of the numbers "a" and "b", then all the multiples of "v" are also multiples of "a" and "b". **- The common multiples of 6 and 15 are the numbers 30, 60, 90, 120, and so on.
- Out of these, 30 is the smallest, 30 is the least common multiple (lcm) of 6 and 15.

- Note: The
**prime factorization** of a number: finding the prime numbers that multiply together to give that number. **If e = lcm (a, b), then the prime factorization of "e" must contain all the prime factors involved in the prime factorization of "a" and "b" taken by the highest power. **

**Example: **
- 40 = 2
^{3} × 5
- 36 = 2
^{2} × 3^{2}
- 126 = 2 × 3
^{2} × 7
- lcm (40, 36, 126) = 2
^{3} × 3^{2} × 5 × 7 = 2,520
**Note: **2^{3} = 2 × 2 × 2 = 8. We are saying that 2 was raised to the power of 3. Or, shorter, 2 to the power of 3. In this example 3 is the exponent and 2 is the base. The exponent indicates how many times the base is multiplied by itself. 2^{3} is the power and 8 is the value of the power:

**Another example of calculating the least common multiple, lcm: **
- 938 = 2 × 7 × 67
- 982 = 2 × 491
- 743 = is a prime number and cannot be broken down into other prime factors
- lcm (938, 982, 743) = 2 × 7 × 67 × 491 × 743 = 342,194,594

**If two or more numbers have no common factors (they are coprime)**, then their least common multiple is calculated by simply multiplying the numbers. - Example:
- 6 = 2 × 3
- 35 = 5 × 7
- lcm (6, 35) = 2 × 3 × 5 × 7 = 6 × 35 = 210

## Some articles on the prime numbers