Free LCM Calculator determines the least common multiple (LCM) between 34 and 42 the smallest integer that is 714 that is divisible by both numbers.

Least Common Multiple (LCM) of 34 and 42 is **714**.

LCM(34,42) = 714

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

- Least Common Multiple of 34 and 42 by Prime method
- Least Common Multiple of 34 and 42 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 34 and 42. First we will calculate the **prime factors of 34 and 42**.

**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}

**Prime Factorization of 42**

2 | 42 |

3 | 21 |

7 | 7 |

1 |

Prime factors of 42 are 2, 3,7. Prime factorization of **42** in exponential form is:

42 = 2^{1}×3^{1}×7^{1}

Now multiplying the highest exponent prime factors to calculate the **LCM of 34 and 42**.

LCM(34,42) = 2^{1}×3^{1}×7^{1}×17^{1}

LCM(34,42) = 714

**Factors of 34**

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

1, 2, 17, 34

**Factors of 42**

List of positive integer factors of 42 that divides 42 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42

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

We need to calculate greatest common factor 34 and 42, than apply into the LCM equation.

GCF(34,42) = 2

LCM(34,42) = ( 34 × 42) / 2

LCM(34,42) = 1428 / 2

LCM(34,42) = 714

(i) The LCM of 42 and 34 is associative

LCM of 34 and 42 = LCM of 42 and 34

1. What is the LCM of 34 and 42?

Answer: LCM of 34 and 42 is 714.

2. 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.

3. What are the Factors of 42?

Answer: Factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42. There are 8 integers that are factors of 42. The greatest factor of 42 is 42.

4. How to Find the LCM of 34 and 42?

Answer:

Least Common Multiple of 34 and 42 = 714

Step 1: Find the prime factorization of 34

34 = 2 x 17

Step 2: Find the prime factorization of 42

42 = 2 x 3 x 7

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

LCM = 714 = 2 x 3 x 7 x 17

Step 4: Therefore, the least common multiple of 34 and 42 is 714.