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

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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 common multiple.

Example: LCM for 10 and 12

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 common multiple is 60.

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

Example: \( 10 = 2 \times 5 \) and \( 12 = 2 \times 2 \times 3 \)

Common factors : 2 and 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)

Example: GCD(10, 12) = 2

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

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

Example: LCM for 10, 12 and 15

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 common multiple is 60.

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

Example: LCM(10, 12) = 60

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

To calculate fractions and/or set fractions with the same denominator, calculate the lowest common multiple of the denominators (the fraction below the fraction line).

Example: The fractions 7/8 and 15/36, their smallest common denominator is LCM(8,36)=72.

7/8 can therefore be written as 63/72 and 15/36 can be written 30/72.

Calculators has generally a function for LCM, else with GCD function, apply the formula:

$$$ LCM(a, b) = a * b / GCD(a, b) $$$

0 has no multiple, because no number can be divided 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.

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

The following numbers have the property of having many divisors, some of them are highly composite numbers.

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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- Calculus of LCM of any numbers
- Calculus of LCM of fractions
- How to calculate the LCM? (Algorithm)
- How to calculate the LCM with multiple numbers? (LCM of 2 numbers or more)
- How to calculate the lowest common denominator of fractions?
- How to calculate LCM with a calculator (TI or Casio)?
- How to calculate LCM with a zero 0?
- How to calculate LCM with non-integers?
- What are LCM for the N first integers?

lcm,gcd,lowest,smallest,common,multiple,divisor,algorithm,fraction,integer

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