Tool to calculate LCM. The lowest common multiple of two integers a and b is the smallest integer than is multiple of these two numbers.

LCM (Lowest Common Multiple) - dCode

Tag(s) : Arithmetics,Mathematics

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Tool to calculate LCM. The lowest common multiple of two integers a and b is the smallest integer than is multiple of these two numbers.

Method 1: list multiples and find the lowest commun multiple.

Let the numbers be 10 and 12, one wants to find the LCM

10 has for multiples 0,10,20,30,40,50,60,70 etc.

12 has for multiples 0,12,24,36,48,60,72 etc.

The lowest commun multiple is 60.

Method 2: use the prime factors decomposition. The LCM is the multiplication of common factors by non common factors

10 = 2 * 5

12 = 2 * 2 * 3

Common factors : 2

Non common factors : 2, 3, 5

LCM(10, 12) = 2 * 2 * 3 * 5 = 60

Method 3: use the GCD value and use the formula LCM(a, b) = a * b / GCD(a, b)

GCD(10, 12) = 2

LCM(10, 12) = (10 * 12) / 2 = 60

Method 1: list multiples and find the lowest commun multiple.

Let the numbers be 10 and 12, one wants to find the LCM

10 has for multiples 0,10,20,30,40,50,60,70 etc.

12 has for multiples 0,12,24,36,48,60,72 etc.

15 has for multiples 0,15,30,45,60,75 etc.

The lowest commun multiple is 60.

Method 2: use the formula LCM(a,b,c) = LCM( LCM(a,b), c)

LCM(10, 12) = 60

LCM(10, 12, 15) = LCM ( LCM(10, 12) , 15 ) = LCM(60,15) = 60

0 has no multiple, because no number can be devided by zero

LCM as it is mathematically defined, has no sense with non integers. However, it is possible to use this formula: CM(a*c,b*c) = CM(a,b)*c where CM is a common multiple (not the lowest) other rational numbers.

CM(1.2,2.4) = CM(12,24)/10 = 2

LCM(1,2,3)= | 6 |

LCM(1,2,3,4)= | 12 |

LCM(1,2,3,4,5)= | 60 |

LCM(1,2,3,4,5,6)= | 60 |

LCM(1,2,3...6,7)= | 420 |

LCM(1,2,3...7,8)= | 840 |

LCM(1,2,3...8,9)= | 2520 |

LCM(1,2,3...9,10)= | 2520 |

LCM(1,2,3...10,11)= | 27720 |

LCM(1,2,3...11,12)= | 27720 |

LCM(1,2,3...12,13)= | 360360 |

LCM(1,2,3...13,14)= | 360360 |

LCM(1,2,3...14,15)= | 360360 |

LCM(1,2,3...15,16)= | 720720 |

LCM(1,2,3...16,17)= | 12252240 |

LCM(1,2,3...17,18)= | 12252240 |

LCM(1,2,3...18,19)= | 232792560 |

LCM(1,2,3...19,20)= | 232792560 |

LCM(1,2,3...20,21)= | 232792560 |

LCM(1,2,3...21,22)= | 232792560 |

LCM(1,2,3...22,23)= | 5354228880 |

LCM(1,2,3...23,24)= | 5354228880 |

LCM(1,2,3...24,25)= | 26771144400 |

LCM(1,2,3...25,26)= | 26771144400 |

LCM(1,2,3...26,27)= | 80313433200 |

LCM(1,2,3...27,28)= | 80313433200 |

LCM(1,2,3...28,29)= | 2329089562800 |

LCM(1,2,3...29,30)= | 2329089562800 |

LCM(1,2,3...30,31)= | 72201776446800 |

LCM(1,2,3...31,32)= | 144403552893600 |

LCM(1,2,3...32,33)= | 144403552893600 |

LCM(1,2,3...33,34)= | 144403552893600 |

LCM(1,2,3...34,35)= | 144403552893600 |

LCM(1,2,3...35,36)= | 144403552893600 |

LCM(1,2,3...36,37)= | 5342931457063200 |

LCM(1,2,3...37,38)= | 5342931457063200 |

LCM(1,2,3...38,39)= | 5342931457063200 |

LCM(1,2,3...39,40)= | 5342931457063200 |

LCM(1,2,3...40,41)= | 219060189739591200 |

LCM(1,2,3...41,42)= | 219060189739591200 |

LCM(1,2,3...42,43)= | 9419588158802421600 |

LCM(1,2,3...43,44)= | 9419588158802421600 |

LCM(1,2,3...44,45)= | 9419588158802421600 |

LCM(1,2,3...45,46)= | 9419588158802421600 |

LCM(1,2,3...46,47)= | 442720643463713815200 |

LCM(1,2,3...47,48)= | 442720643463713815200 |

LCM(1,2,3...48,49)= | 3099044504245996706400 |

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