Free LCM Calculator determines the least common multiple (LCM) between 3 and 9 the smallest integer that is 9 that is divisible by both numbers.

Least Common Multiple (LCM) of 3 and 9 is **9**.

LCM(3,9) = 9

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

Least common multiple can be found by multiplying the highest exponent prime factors of 3 and 9. First we will calculate the **prime factors of 3 and 9**.

**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 9**

3 | 9 |

3 | 3 |

1 |

Prime factors of 9 are 3. Prime factorization of **9** in exponential form is:

9 = 3^{2}

Now multiplying the highest exponent prime factors to calculate the **LCM of 3 and 9**.

LCM(3,9) = 3^{2}

LCM(3,9) = 9

**Factors of 3**

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

1, 3

**Factors of 9**

List of positive integer factors of 9 that divides 9 without a remainder.

1, 3, 9

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

We need to calculate greatest common factor 3 and 9, than apply into the LCM equation.

GCF(3,9) = 3

LCM(3,9) = ( 3 × 9) / 3

LCM(3,9) = 27 / 3

LCM(3,9) = 9

**Multiples of 3**

3, 6,9

**Multiples of 9**

9

Find the smallest number that is on all of the lists. We have it in bold above.

∴ Least Common Multiple of 3 and 9 is 9

(i) The LCM of 9 and 3 is associative

LCM of 3 and 9 = LCM of 9 and 3

1. What is the LCM of 3 and 9?

Answer: LCM of 3 and 9 is 9.

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 9?

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

4. How to Find the LCM of 3 and 9?

Answer:

Least Common Multiple of 3 and 9 = 9

Step 1: Find the prime factorization of 3

3 = 3

Step 2: Find the prime factorization of 9

9 = 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 = 9 = 3 x 3

Step 4: Therefore, the least common multiple of 3 and 9 is 9.