Free LCM Calculator determines the least common multiple (LCM) between 12 and 18 the smallest integer that is 36 that is divisible by both numbers.

Least Common Multiple (LCM) of 12 and 18 is **36**.

LCM(12,18) = 36

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

- Least Common Multiple of 12 and 18 by Prime method
- Least Common Multiple of 12 and 18 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 12 and 18. First we will calculate the **prime factors of 12 and 18**.

**Prime Factorization of 12**

2 | 12 |

2 | 6 |

3 | 3 |

1 |

Prime factors of 12 are 2,3. Prime factorization of **12** in exponential form is:

12 = 2^{2}×3^{1}

**Prime Factorization of 18**

2 | 18 |

3 | 9 |

3 | 3 |

1 |

Prime factors of 18 are 2,3. Prime factorization of **18** in exponential form is:

18 = 2^{1}×3^{2}

Now multiplying the highest exponent prime factors to calculate the **LCM of 12 and 18**.

LCM(12,18) = 2^{2}×3^{2}

LCM(12,18) = 36

**Factors of 12**

List of positive integer factors of 12 that divides 12 without a remainder.

1, 2, 3, 4, 6, 12

**Factors of 18**

List of positive integer factors of 18 that divides 18 without a remainder.

1, 2, 3, 6, 9, 18

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

We need to calculate greatest common factor 12 and 18, than apply into the LCM equation.

GCF(12,18) = 6

LCM(12,18) = ( 12 × 18) / 6

LCM(12,18) = 216 / 6

LCM(12,18) = 36

(i) The LCM of 18 and 12 is associative

LCM of 12 and 18 = LCM of 18 and 12

1. What is the LCM of 12 and 18?

Answer: LCM of 12 and 18 is 36.

2. What are the Factors of 12?

Answer: Factors of 12 are 1, 2, 3, 4, 6, 12. There are 6 integers that are factors of 12. The greatest factor of 12 is 12.

3. What are the Factors of 18?

Answer: Factors of 18 are 1, 2, 3, 6, 9, 18. There are 6 integers that are factors of 18. The greatest factor of 18 is 18.

4. How to Find the LCM of 12 and 18?

Answer:

Least Common Multiple of 12 and 18 = 36

Step 1: Find the prime factorization of 12

12 = 2 x 2 x 3

Step 2: Find the prime factorization of 18

18 = 2 x 3 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 = 36 = 2 x 2 x 3 x 3

Step 4: Therefore, the least common multiple of 12 and 18 is 36.