**Created By :**
Jatin Gogia

**Reviewed By :**
Rajasekhar Valipishetty

**Last Updated :**
Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 33 and 39 the smallest integer that is 429 that is divisible by both numbers.

Least Common Multiple (LCM) of 33 and 39 is **429**.

LCM(33,39) = 429

*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 33 and 39. First we will calculate the **prime factors of 33 and 39**.

**Prime Factorization of 33**

3 | 33 |

11 | 11 |

1 |

Prime factors of 33 are 3,11. Prime factorization of **33** in exponential form is:

33 = 3^{1}×11^{1}

**Prime Factorization of 39**

3 | 39 |

13 | 13 |

1 |

Prime factors of 39 are 3,13. Prime factorization of **39** in exponential form is:

39 = 3^{1}×13^{1}

Now multiplying the highest exponent prime factors to calculate the **LCM of 33 and 39**.

LCM(33,39) = 3^{1}×11^{1}×13^{1}

LCM(33,39) = 429

**Factors of 33**

List of positive integer factors of 33 that divides 33 without a remainder.

1, 3, 11, 33

**Factors of 39**

List of positive integer factors of 39 that divides 39 without a remainder.

1, 3, 13, 39

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

We need to calculate greatest common factor 33 and 39, than apply into the LCM equation.

GCF(33,39) = 3

LCM(33,39) = ( 33 × 39) / 3

LCM(33,39) = 1287 / 3

LCM(33,39) = 429

(i) The LCM of 39 and 33 is associative

LCM of 33 and 39 = LCM of 39 and 33

1. What is the LCM of 33 and 39?

Answer: LCM of 33 and 39 is 429.

2. What are the Factors of 33?

Answer: Factors of 33 are 1, 3, 11, 33. There are 4 integers that are factors of 33. The greatest factor of 33 is 33.

3. What are the Factors of 39?

Answer: Factors of 39 are 1, 3, 13, 39. There are 4 integers that are factors of 39. The greatest factor of 39 is 39.

4. How to Find the LCM of 33 and 39?

Answer:

Least Common Multiple of 33 and 39 = 429

Step 1: Find the prime factorization of 33

33 = 3 x 11

Step 2: Find the prime factorization of 39

39 = 3 x 13

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

LCM = 429 = 3 x 11 x 13

Step 4: Therefore, the least common multiple of 33 and 39 is 429.