**Created By :**
Jatin Gogia

**Reviewed By :**
Rajasekhar Valipishetty

**Last Updated :**
Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 15 and 22 the smallest integer that is 330 that is divisible by both numbers.

Least Common Multiple (LCM) of 15 and 22 is **330**.

LCM(15,22) = 330

*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 15 and 22. First we will calculate the **prime factors of 15 and 22**.

**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}

**Prime Factorization of 22**

2 | 22 |

11 | 11 |

1 |

Prime factors of 22 are 2,11. Prime factorization of **22** in exponential form is:

22 = 2^{1}×11^{1}

Now multiplying the highest exponent prime factors to calculate the **LCM of 15 and 22**.

LCM(15,22) = 2^{1}×3^{1}×5^{1}×11^{1}

LCM(15,22) = 330

**Factors of 15**

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

1, 3, 5, 15

**Factors of 22**

List of positive integer factors of 22 that divides 22 without a remainder.

1, 2, 11, 22

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

We need to calculate greatest common factor 15 and 22, than apply into the LCM equation.

GCF(15,22) = 1

LCM(15,22) = ( 15 × 22) / 1

LCM(15,22) = 330 / 1

LCM(15,22) = 330

(i) The LCM of 22 and 15 is associative

LCM of 15 and 22 = LCM of 22 and 15

1. What is the LCM of 15 and 22?

Answer: LCM of 15 and 22 is 330.

2. 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.

3. What are the Factors of 22?

Answer: Factors of 22 are 1, 2, 11, 22. There are 4 integers that are factors of 22. The greatest factor of 22 is 22.

4. How to Find the LCM of 15 and 22?

Answer:

Least Common Multiple of 15 and 22 = 330

Step 1: Find the prime factorization of 15

15 = 3 x 5

Step 2: Find the prime factorization of 22

22 = 2 x 11

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

LCM = 330 = 2 x 3 x 5 x 11

Step 4: Therefore, the least common multiple of 15 and 22 is 330.