Free LCM Calculator determines the least common multiple (LCM) between 9 and 15 the smallest integer that is 45 that is divisible by both numbers.

Least Common Multiple (LCM) of 9 and 15 is **45**.

LCM(9,15) = 45

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

- Least Common Multiple of 9 and 15 by Prime method
- Least Common Multiple of 9 and 15 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 9 and 15. First we will calculate the **prime factors of 9 and 15**.

**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}

**Prime Factorization of 15**

3 | 15 |

5 | 5 |

1 |

Prime factors of 15 are 3,5. Prime factorization of **15** in exponential form is:

15 = 3^{1}×5^{1}

Now multiplying the highest exponent prime factors to calculate the **LCM of 9 and 15**.

LCM(9,15) = 3^{2}×5^{1}

LCM(9,15) = 45

**Factors of 9**

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

1, 3, 9

**Factors of 15**

List of positive integer factors of 15 that divides 15 without a remainder.

1, 3, 5, 15

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

We need to calculate greatest common factor 9 and 15, than apply into the LCM equation.

GCF(9,15) = 3

LCM(9,15) = ( 9 × 15) / 3

LCM(9,15) = 135 / 3

LCM(9,15) = 45

(i) The LCM of 15 and 9 is associative

LCM of 9 and 15 = LCM of 15 and 9

1. What is the LCM of 9 and 15?

Answer: LCM of 9 and 15 is 45.

2. 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.

3. What are the Factors of 15?

Answer: Factors of 15 are 1, 3, 5, 15. There are 4 integers that are factors of 15. The greatest factor of 15 is 15.

4. How to Find the LCM of 9 and 15?

Answer:

Least Common Multiple of 9 and 15 = 45

Step 1: Find the prime factorization of 9

9 = 3 x 3

Step 2: Find the prime factorization of 15

15 = 3 x 5

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

LCM = 45 = 3 x 3 x 5

Step 4: Therefore, the least common multiple of 9 and 15 is 45.