Free LCM Calculator determines the least common multiple (LCM) between 20 and 30 the smallest integer that is 60 that is divisible by both numbers.

Least Common Multiple (LCM) of 20 and 30 is **60**.

LCM(20,30) = 60

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

- Least Common Multiple of 20 and 30 by Prime method
- Least Common Multiple of 20 and 30 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 20 and 30. First we will calculate the **prime factors of 20 and 30**.

**Prime Factorization of 20**

2 | 20 |

2 | 10 |

5 | 5 |

1 |

Prime factors of 20 are 2,5. Prime factorization of **20** in exponential form is:

20 = 2^{2}×5^{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 20 and 30**.

LCM(20,30) = 2^{2}×3^{1}×5^{1}

LCM(20,30) = 60

**Factors of 20**

List of positive integer factors of 20 that divides 20 without a remainder.

1, 2, 4, 5, 10, 20

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

GCF(20,30) = 10

LCM(20,30) = ( 20 × 30) / 10

LCM(20,30) = 600 / 10

LCM(20,30) = 60

(i) The LCM of 30 and 20 is associative

LCM of 20 and 30 = LCM of 30 and 20

1. What is the LCM of 20 and 30?

Answer: LCM of 20 and 30 is 60.

2. What are the Factors of 20?

Answer: Factors of 20 are 1, 2, 4, 5, 10, 20. There are 6 integers that are factors of 20. The greatest factor of 20 is 20.

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 20 and 30?

Answer:

Least Common Multiple of 20 and 30 = 60

Step 1: Find the prime factorization of 20

20 = 2 x 2 x 5

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 = 60 = 2 x 2 x 3 x 5

Step 4: Therefore, the least common multiple of 20 and 30 is 60.