# Calculate the Least Common Multiple or LCM of 112, 84 and 27

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The instructions to find the LCM of 112, 84 and 27 are the next:

## 1. Decompose all numbers into prime factors

112 | 2 |

56 | 2 |

28 | 2 |

14 | 2 |

7 | 7 |

1 |

84 | 2 |

42 | 2 |

21 | 3 |

7 | 7 |

1 |

27 | 3 |

9 | 3 |

3 | 3 |

1 |

## 2. Write all numbers as the product of its prime factors

Prime factors of 112 | = | 2^{4} . 7 |

Prime factors of 84 | = | 2^{2} . 3 . 7 |

Prime factors of 27 | = | 3^{3} |

## 3. Choose the common and uncommon prime factors with the greatest exponent

Common prime factors: None

Common prime factors with the greatest exponent: None

Uncommon prime factors: 2 , 7 , 3

Uncommon prime factors with the greatest exponent: 2^{4}, 7^{1}, 3^{3}

## 4. Calculate the Least Common Multiple or LCM

Remember, to find the LCM of several numbers you must multiply the common and uncommon prime factors with the greatest exponent of those numbers.

**LCM** = 2^{4}. 7^{1}. 3^{3} = 3024

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