# Calculate LCM & GCF

## About This Calculator

This calculator makes it easy to quickly estimate the least common multiple and greatest comon factor for up to three numbers at a time.

### Calculating Least Common Multiple (LCM) / Least Common Divisor (LCD)

There are multiple ways to calculate LCM including:

**listing multiples:**Create lists of multiples for each numbers and compare where they overlap**prime factorization:**List each prime factor of a number using exponent notation. Multiply all prime factors together while repeating each factor by whichever exponent level is highest for that prime**cake / ladder:**Divide numbers by prime numbers as long as two numbers remain evenly divisible by that number then carry down any numbers that are not divsible by that factor. multiply the factors by the remainders to obtain the LCM.**division method:**Write your numbers in the top row of a division table and keep dividing by each prime number until the result is no longer divisible. Then divide by increasing prime numbers. Once the bottom row is all ones find the product from the left column**greatest common factor:**Divide the largest number shared by all the factors

### Example Calculation

Find the LCM for 4, 6, and 15

#### Listing Multiples

Multiples of 4:

4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, ** 60**, 64, 68

Multiples of 6:

6, 12, 18, 24, 30, 36, 42, 48, 54, ** 60**, 66, 72

Multiples of 15:

15, 30, 45, ** 60**, 75, 90

#### Prime Factorization

Prime Factorization of 4 is:

2 x 2 => 2^{2}

Prime Factorization of 6 is:

2 x 3 => 2^{1} x 3^{1}

Prime Factorization of 15 is:

3 x 5 => 3^{1} x 5^{1}

LCM = 2 x 2 x 3 x 5 = 60

In exponential form:

LCM = 2^{2} x 3^{1} x 5^{1} = 60

LCM = 60

#### Cake / Ladder

2 |
4 | 6 | 15 |

3 |
2 | 3 | 15 |

2 |
1 |
5 |

LCM = 2 x 3 x 2 x 5 = 60

#### Division Method

Division Table

2 |
4 | 6 | 15 |

2 |
2 | 3 | 15 |

3 |
1 | 3 | 15 |

5 |
1 | 1 | 5 |

1 |
1 |
1 |

LCM = 2 x 2 x 3 x 5 = 60

#### Greatest Common Factor

LCM(4, 6, 15) = LCM(LCM(4, 6), 15)

LCM(4,6) = (4 × 6) / GCF(4,6)

= (4 × 6) / 2

= 24 / 2

= 12

LCM(12,15) = (12 × 15) / GCF(12,15)

= (12 × 15) / 3

= 180 / 3

= 60