# Calculate the Least Common Multiple or LCM of 38, 350, 70, 19, 11 and 54

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The instructions to find the LCM of 38, 350, 70, 19, 11 and 54 are the next:

## 1. Decompose all numbers into prime factors

38 | 2 |

19 | 19 |

1 |

350 | 2 |

175 | 5 |

35 | 5 |

7 | 7 |

1 |

70 | 2 |

35 | 5 |

7 | 7 |

1 |

19 | 19 |

1 |

11 | 11 |

1 |

54 | 2 |

27 | 3 |

9 | 3 |

3 | 3 |

1 |

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

Prime factors of 38 | = | 2 . 19 |

Prime factors of 350 | = | 2 . 5^{2} . 7 |

Prime factors of 70 | = | 2 . 5 . 7 |

Prime factors of 19 | = | 19 |

Prime factors of 11 | = | 11 |

Prime factors of 54 | = | 2 . 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 , 19 , 5 , 7 , 11 , 3

Uncommon prime factors with the greatest exponent: 2^{1}, 19^{1}, 5^{2}, 7^{1}, 11^{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^{1}. 19^{1}. 5^{2}. 7^{1}. 11^{1}. 3^{3} = 1975050

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