Free LCM Calculator determines the least common multiple (LCM) between 189 and 192 the smallest integer that is 12096 that is divisible by both numbers.

Least Common Multiple (LCM) of 189 and 192 is **12096**.

LCM(189,192) = 12096

*Least common multiple* or lowest common denominator (LCD) can be calculated in three ways;

- Least Common Multiple of 189 and 192 by Prime method
- Least Common Multiple of 189 and 192 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 189 and 192. First we will calculate the **prime factors of 189 and 192**.

**Prime Factorization of 189**

3 | 189 |

3 | 63 |

3 | 21 |

7 | 7 |

1 |

Prime factors of 189 are 3,7. Prime factorization of **189** in exponential form is:

189 = 3^{3}×7^{1}

**Prime Factorization of 192**

2 | 192 |

2 | 96 |

2 | 48 |

2 | 24 |

2 | 12 |

2 | 6 |

3 | 3 |

1 |

Prime factors of 192 are 2,3. Prime factorization of **192** in exponential form is:

192 = 2^{6}×3^{1}

Now multiplying the highest exponent prime factors to calculate the **LCM of 189 and 192**.

LCM(189,192) = 2^{6}×3^{3}×7^{1}

LCM(189,192) = 12096

**Factors of 189**

List of positive integer factors of 189 that divides 189 without a remainder.

1, 3, 7, 9, 21, 27, 63, 189

**Factors of 192**

List of positive integer factors of 192 that divides 192 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192

The formula of **LCM** is LCM(a,b) = ( a × b) / GCF(a,b).

We need to calculate greatest common factor 189 and 192, than apply into the LCM equation.

GCF(189,192) = 3

LCM(189,192) = ( 189 × 192) / 3

LCM(189,192) = 36288 / 3

LCM(189,192) = 12096

(i) The LCM of 192 and 189 is associative

LCM of 189 and 192 = LCM of 192 and 189

1. What is the LCM of 189 and 192?

Answer: LCM of 189 and 192 is 12096.

2. What are the Factors of 189?

Answer: Factors of 189 are 1, 3, 7, 9, 21, 27, 63, 189. There are 8 integers that are factors of 189. The greatest factor of 189 is 189.

3. What are the Factors of 192?

Answer: Factors of 192 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192. There are 14 integers that are factors of 192. The greatest factor of 192 is 192.

4. How to Find the LCM of 189 and 192?

Answer:

Least Common Multiple of 189 and 192 = 12096

Step 1: Find the prime factorization of 189

189 = 3 x 3 x 3 x 7

Step 2: Find the prime factorization of 192

192 = 2 x 2 x 2 x 2 x 2 x 2 x 3

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 12096 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 7

Step 4: Therefore, the least common multiple of 189 and 192 is 12096.