**Created By :**
Jatin Gogia

**Reviewed By :**
Rajasekhar Valipishetty

**Last Updated :**
Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 27 and 34 the smallest integer that is 918 that is divisible by both numbers.

Least Common Multiple (LCM) of 27 and 34 is **918**.

LCM(27,34) = 918

*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 27 and 34. First we will calculate the **prime factors of 27 and 34**.

**Prime Factorization of 27**

3 | 27 |

3 | 9 |

3 | 3 |

1 |

Prime factors of 27 are 3. Prime factorization of **27** in exponential form is:

27 = 3^{3}

**Prime Factorization of 34**

2 | 34 |

17 | 17 |

1 |

Prime factors of 34 are 2,17. Prime factorization of **34** in exponential form is:

34 = 2^{1}×17^{1}

Now multiplying the highest exponent prime factors to calculate the **LCM of 27 and 34**.

LCM(27,34) = 2^{1}×3^{3}×17^{1}

LCM(27,34) = 918

**Factors of 27**

List of positive integer factors of 27 that divides 27 without a remainder.

1, 3, 9, 27

**Factors of 34**

List of positive integer factors of 34 that divides 34 without a remainder.

1, 2, 17, 34

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

We need to calculate greatest common factor 27 and 34, than apply into the LCM equation.

GCF(27,34) = 1

LCM(27,34) = ( 27 × 34) / 1

LCM(27,34) = 918 / 1

LCM(27,34) = 918

(i) The LCM of 34 and 27 is associative

LCM of 27 and 34 = LCM of 34 and 27

1. What is the LCM of 27 and 34?

Answer: LCM of 27 and 34 is 918.

2. What are the Factors of 27?

Answer: Factors of 27 are 1, 3, 9, 27. There are 4 integers that are factors of 27. The greatest factor of 27 is 27.

3. What are the Factors of 34?

Answer: Factors of 34 are 1, 2, 17, 34. There are 4 integers that are factors of 34. The greatest factor of 34 is 34.

4. How to Find the LCM of 27 and 34?

Answer:

Least Common Multiple of 27 and 34 = 918

Step 1: Find the prime factorization of 27

27 = 3 x 3 x 3

Step 2: Find the prime factorization of 34

34 = 2 x 17

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

LCM = 918 = 2 x 3 x 3 x 3 x 17

Step 4: Therefore, the least common multiple of 27 and 34 is 918.