Free LCM Calculator determines the least common multiple (LCM) between 30 and 34 the smallest integer that is 510 that is divisible by both numbers.

Least Common Multiple (LCM) of 30 and 34 is **510**.

LCM(30,34) = 510

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

- Least Common Multiple of 30 and 34 by Prime method
- Least Common Multiple of 30 and 34 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 30 and 34. First we will calculate the **prime factors of 30 and 34**.

**Prime Factorization of 30**

2 | 30 |

3 | 15 |

5 | 5 |

1 |

Prime factors of 30 are 2, 3,5. Prime factorization of **30** in exponential form is:

30 = 2^{1}×3^{1}×5^{1}

**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 30 and 34**.

LCM(30,34) = 2^{1}×3^{1}×5^{1}×17^{1}

LCM(30,34) = 510

**Factors of 30**

List of positive integer factors of 30 that divides 30 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30

**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 30 and 34, than apply into the LCM equation.

GCF(30,34) = 2

LCM(30,34) = ( 30 × 34) / 2

LCM(30,34) = 1020 / 2

LCM(30,34) = 510

(i) The LCM of 34 and 30 is associative

LCM of 30 and 34 = LCM of 34 and 30

1. What is the LCM of 30 and 34?

Answer: LCM of 30 and 34 is 510.

2. What are the Factors of 30?

Answer: Factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30. There are 8 integers that are factors of 30. The greatest factor of 30 is 30.

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 30 and 34?

Answer:

Least Common Multiple of 30 and 34 = 510

Step 1: Find the prime factorization of 30

30 = 2 x 3 x 5

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 = 510 = 2 x 3 x 5 x 17

Step 4: Therefore, the least common multiple of 30 and 34 is 510.