Free LCM Calculator determines the least common multiple (LCM) between 3 and 12 the smallest integer that is 12 that is divisible by both numbers.

Least Common Multiple (LCM) of 3 and 12 is **12**.

LCM(3,12) = 12

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

- Least Common Multiple of 3 and 12 by Prime method
- Least Common Multiple of 3 and 12 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 3 and 12. First we will calculate the **prime factors of 3 and 12**.

**Prime Factorization of 3**

3 | 3 |

1 |

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

3 = 3^{1}

**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}

Now multiplying the highest exponent prime factors to calculate the **LCM of 3 and 12**.

LCM(3,12) = 2^{2}×3^{1}

LCM(3,12) = 12

**Factors of 3**

List of positive integer factors of 3 that divides 3 without a remainder.

1, 3

**Factors of 12**

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

1, 2, 3, 4, 6, 12

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

We need to calculate greatest common factor 3 and 12, than apply into the LCM equation.

GCF(3,12) = 3

LCM(3,12) = ( 3 × 12) / 3

LCM(3,12) = 36 / 3

LCM(3,12) = 12

(i) The LCM of 12 and 3 is associative

LCM of 3 and 12 = LCM of 12 and 3

1. What is the LCM of 3 and 12?

Answer: LCM of 3 and 12 is 12.

2. What are the Factors of 3?

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

3. 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.

4. How to Find the LCM of 3 and 12?

Answer:

Least Common Multiple of 3 and 12 = 12

Step 1: Find the prime factorization of 3

3 = 3

Step 2: Find the prime factorization of 12

12 = 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 = 12 = 2 x 2 x 3

Step 4: Therefore, the least common multiple of 3 and 12 is 12.