**Created By :**
Jatin Gogia

**Reviewed By :**
Rajasekhar Valipishetty

**Last Updated :**
Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 2 and 9 the smallest integer that is 18 that is divisible by both numbers.

Least Common Multiple (LCM) of 2 and 9 is **18**.

LCM(2,9) = 18

*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 2 and 9. First we will calculate the **prime factors of 2 and 9**.

**Prime Factorization of 2**

2 | 2 |

1 |

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

2 = 2^{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 2 and 9**.

LCM(2,9) = 2^{1}×3^{2}

LCM(2,9) = 18

**Factors of 2**

List of positive integer factors of 2 that divides 2 without a remainder.

1, 2

**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 2 and 9, than apply into the LCM equation.

GCF(2,9) = 1

LCM(2,9) = ( 2 × 9) / 1

LCM(2,9) = 18 / 1

LCM(2,9) = 18

(i) The LCM of 9 and 2 is associative

LCM of 2 and 9 = LCM of 9 and 2

1. What is the LCM of 2 and 9?

Answer: LCM of 2 and 9 is 18.

2. What are the Factors of 2?

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

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 2 and 9?

Answer:

Least Common Multiple of 2 and 9 = 18

Step 1: Find the prime factorization of 2

2 = 2

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 = 18 = 2 x 3 x 3

Step 4: Therefore, the least common multiple of 2 and 9 is 18.