# Calculate the Least Common Multiple or LCM of 54, 20 and 8

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The instructions to find the LCM of 54, 20 and 8 are the next:

## 1. Decompose all numbers into prime factors

54 | 2 |

27 | 3 |

9 | 3 |

3 | 3 |

1 |

20 | 2 |

10 | 2 |

5 | 5 |

1 |

8 | 2 |

4 | 2 |

2 | 2 |

1 |

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

Prime factors of 54 | = | 2 . 3^{3} |

Prime factors of 20 | = | 2^{2} . 5 |

Prime factors of 8 | = | 2^{3} |

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

Common prime factors: 2

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

Uncommon prime factors: 3 , 5

Uncommon prime factors with the greatest exponent: 3^{3}, 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** = 2^{3}. 3^{3}. 5^{1} = 1080

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