# Calculate the Least Common Multiple or LCM of 3, 12, 27 and 45

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The instructions to find the LCM of 3, 12, 27 and 45 are the next:

## 1. Decompose all numbers into prime factors

3 | 3 |

1 |

12 | 2 |

6 | 2 |

3 | 3 |

1 |

27 | 3 |

9 | 3 |

3 | 3 |

1 |

45 | 3 |

15 | 3 |

5 | 5 |

1 |

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

Prime factors of 3 | = | 3 |

Prime factors of 12 | = | 2^{2} . 3 |

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

Prime factors of 45 | = | 3^{2} . 5 |

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

Common prime factors: 3

Common prime factors with the greatest exponent: 3^{3}

Uncommon prime factors: 2 , 5

Uncommon prime factors with the greatest exponent: 2^{2}, 5^{1}

## 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** = 3^{3}. 2^{2}. 5^{1} = 540

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