LCM of 5 and 6 is the smallest number among all common multiples of 5 and 6. The first few multiples of 5 and 6 are (5, 10, 15, 20, 25, 30, . . . ) and (6, 12, 18, 24, 30, 36, . . . ) respectively. There are 3 commonly used methods to find LCM of 5 and 6 – by prime factorization, by division method, and by listing multiples.

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1. | LCM of 5 and 6 |

2. | List of Methods |

3. | Solved Examples |

4. | FAQs |

**Answer:** LCM of 5 and 6 is 30.

**Explanation: **

The LCM of two non-zero integers, x(5) and y(6), is the smallest positive integer m(30) that is divisible by both x(5) and y(6) without any remainder.

Let's look at the different methods for finding the LCM of 5 and 6.

By Prime Factorization MethodBy Division MethodBy Listing Multiples

### LCM of 5 and 6 by Prime Factorization

Prime factorization of 5 and 6 is (5) = 51 and (2 × 3) = 21 × 31 respectively. LCM of 5 and 6 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 21 × 31 × 51 = 30.Hence, the LCM of 5 and 6 by prime factorization is 30.

### LCM of 5 and 6 by Division Method

To calculate the LCM of 5 and 6 by the division method, we will divide the numbers(5, 6) by their prime factors (preferably common). The product of these divisors gives the LCM of 5 and 6.

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**Step 3:** Continue the steps until only 1s are left in the last row.

The LCM of 5 and 6 is the product of all prime numbers on the left, i.e. LCM(5, 6) by division method = 2 × 3 × 5 = 30.

### LCM of 5 and 6 by Listing Multiples

To calculate the LCM of 5 and 6 by listing out the common multiples, we can follow the given below steps:

**Step 1:** List a few multiples of 5 (5, 10, 15, 20, 25, 30, . . . ) and 6 (6, 12, 18, 24, 30, 36, . . . . )**Step 2:** The common multiples from the multiples of 5 and 6 are 30, 60, . . .**Step 3:** The smallest common multiple of 5 and 6 is 30.

∴ The least common multiple of 5 and 6 = 30.

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## FAQs on LCM of 5 and 6

### What is the LCM of 5 and 6?

The **LCM of 5 and 6 is 30**. To find the least common multiple of 5 and 6, we need to find the multiples of 5 and 6 (multiples of 5 = 5, 10, 15, 20 . . . . 30; multiples of 6 = 6, 12, 18, 24 . . . . 30) and choose the smallest multiple that is exactly divisible by 5 and 6, i.e., 30.

### If the LCM of 6 and 5 is 30, Find its GCF.

LCM(6, 5) × GCF(6, 5) = 6 × 5Since the LCM of 6 and 5 = 30⇒ 30 × GCF(6, 5) = 30Therefore, the greatest common factor = 30/30 = 1.

### What are the Methods to Find LCM of 5 and 6?

The commonly used methods to find the **LCM of 5 and 6** are:

Listing MultiplesPrime Factorization MethodDivision Method

### What is the Relation Between GCF and LCM of 5, 6?

The following equation can be used to express the relation between GCF and LCM of 5 and 6, i.e. GCF × LCM = 5 × 6.

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### Which of the following is the LCM of 5 and 6? 3, 32, 35, 30

The value of LCM of 5, 6 is the smallest common multiple of 5 and 6. The number satisfying the given condition is 30.