**Created By :**
Jatin Gogia

**Reviewed By :**
Rajasekhar Valipishetty

**Last Updated :**
Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 26 and 30 the smallest integer that is 390 that is divisible by both numbers.

Least Common Multiple (LCM) of 26 and 30 is **390**.

LCM(26,30) = 390

*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 26 and 30. First we will calculate the **prime factors of 26 and 30**.

**Prime Factorization of 26**

2 | 26 |

13 | 13 |

1 |

Prime factors of 26 are 2,13. Prime factorization of **26** in exponential form is:

26 = 2^{1}×13^{1}

**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}

Now multiplying the highest exponent prime factors to calculate the **LCM of 26 and 30**.

LCM(26,30) = 2^{1}×3^{1}×5^{1}×13^{1}

LCM(26,30) = 390

**Factors of 26**

List of positive integer factors of 26 that divides 26 without a remainder.

1, 2, 13, 26

**Factors of 30**

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

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

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

We need to calculate greatest common factor 26 and 30, than apply into the LCM equation.

GCF(26,30) = 2

LCM(26,30) = ( 26 × 30) / 2

LCM(26,30) = 780 / 2

LCM(26,30) = 390

(i) The LCM of 30 and 26 is associative

LCM of 26 and 30 = LCM of 30 and 26

1. What is the LCM of 26 and 30?

Answer: LCM of 26 and 30 is 390.

2. What are the Factors of 26?

Answer: Factors of 26 are 1, 2, 13, 26. There are 4 integers that are factors of 26. The greatest factor of 26 is 26.

3. 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.

4. How to Find the LCM of 26 and 30?

Answer:

Least Common Multiple of 26 and 30 = 390

Step 1: Find the prime factorization of 26

26 = 2 x 13

Step 2: Find the prime factorization of 30

30 = 2 x 3 x 5

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

LCM = 390 = 2 x 3 x 5 x 13

Step 4: Therefore, the least common multiple of 26 and 30 is 390.