Free LCM Calculator determines the least common multiple (LCM) between 20 and 27 the smallest integer that is 540 that is divisible by both numbers.

Least Common Multiple (LCM) of 20 and 27 is **540**.

LCM(20,27) = 540

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

- Least Common Multiple of 20 and 27 by Prime method
- Least Common Multiple of 20 and 27 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 20 and 27. First we will calculate the **prime factors of 20 and 27**.

**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 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}

Now multiplying the highest exponent prime factors to calculate the **LCM of 20 and 27**.

LCM(20,27) = 2^{2}×3^{3}×5^{1}

LCM(20,27) = 540

**Factors of 20**

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

1, 2, 4, 5, 10, 20

**Factors of 27**

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

1, 3, 9, 27

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

We need to calculate greatest common factor 20 and 27, than apply into the LCM equation.

GCF(20,27) = 1

LCM(20,27) = ( 20 × 27) / 1

LCM(20,27) = 540 / 1

LCM(20,27) = 540

(i) The LCM of 27 and 20 is associative

LCM of 20 and 27 = LCM of 27 and 20

1. What is the LCM of 20 and 27?

Answer: LCM of 20 and 27 is 540.

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 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.

4. How to Find the LCM of 20 and 27?

Answer:

Least Common Multiple of 20 and 27 = 540

Step 1: Find the prime factorization of 20

20 = 2 x 2 x 5

Step 2: Find the prime factorization of 27

27 = 3 x 3 x 3

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

LCM = 540 = 2 x 2 x 3 x 3 x 3 x 5

Step 4: Therefore, the least common multiple of 20 and 27 is 540.