# Calculate the Least Common Multiple or LCM of 39, 45, 90 and 111

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The instructions to find the LCM of 39, 45, 90 and 111 are the next:

## 1. Decompose all numbers into prime factors

39 | 3 |

13 | 13 |

1 |

45 | 3 |

15 | 3 |

5 | 5 |

1 |

90 | 2 |

45 | 3 |

15 | 3 |

5 | 5 |

1 |

111 | 3 |

37 | 37 |

1 |

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

Prime factors of 39 | = | 3 . 13 |

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

Prime factors of 90 | = | 2 . 3^{2} . 5 |

Prime factors of 111 | = | 3 . 37 |

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

Common prime factors: 3

Common prime factors with the greatest exponent: 3^{2}

Uncommon prime factors: 13 , 5 , 2 , 37

Uncommon prime factors with the greatest exponent: 13^{1}, 5^{1}, 2^{1}, 37^{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^{2}. 13^{1}. 5^{1}. 2^{1}. 37^{1} = 43290

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