# Calculate the Least Common Multiple or LCM of 180, 340, 450 and 500

Sponsors

The instructions to find the LCM of 180, 340, 450 and 500 are the next:

## 1. Decompose all numbers into prime factors

180 | 2 |

90 | 2 |

45 | 3 |

15 | 3 |

5 | 5 |

1 |

340 | 2 |

170 | 2 |

85 | 5 |

17 | 17 |

1 |

450 | 2 |

225 | 3 |

75 | 3 |

25 | 5 |

5 | 5 |

1 |

500 | 2 |

250 | 2 |

125 | 5 |

25 | 5 |

5 | 5 |

1 |

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

Prime factors of 180 | = | 2^{2} . 3^{2} . 5 |

Prime factors of 340 | = | 2^{2} . 5 . 17 |

Prime factors of 450 | = | 2 . 3^{2} . 5^{2} |

Prime factors of 500 | = | 2^{2} . 5^{3} |

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

Common prime factors: 2 , 5

Common prime factors with the greatest exponent: 2^{2}, 5^{3}

Uncommon prime factors: 3 , 17

Uncommon prime factors with the greatest exponent: 3^{2}, 17^{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** = 2^{2}. 5^{3}. 3^{2}. 17^{1} = 76500

Also calculates the: