LCM of 6 and 9 is the smallest number among all common multiples of 6 and 9. The first few multiples of 6 and 9 are (6, 12, 18, 24, 30, . . . ) and (9, 18, 27, 36, . . . ) respectively. There are 3 commonly used methods to find LCM of 6 and 9 – by prime factorization, by division method, and by listing multiples.

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1. | LCM of 6 and 9 |

2. | List of Methods |

3. | Solved Examples |

4. | FAQs |

**Answer:** LCM of 6 and 9 is 18.

**Explanation: **

The LCM of two non-zero integers, x(6) and y(9), is the smallest positive integer m(18) that is divisible by both x(6) and y(9) without any remainder.

The methods to find the LCM of 6 and 9 are explained below.

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By Division MethodBy Listing MultiplesBy Prime Factorization Method

### LCM of 6 and 9 by Division Method

To calculate the LCM of 6 and 9 by the division method, we will divide the numbers(6, 9) by their prime factors (preferably common). The product of these divisors gives the LCM of 6 and 9.

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

The LCM of 6 and 9 is the product of all prime numbers on the left, i.e. LCM(6, 9) by division method = 2 × 3 × 3 = 18.

### LCM of 6 and 9 by Listing Multiples

To calculate the LCM of 6 and 9 by listing out the common multiples, we can follow the given below steps:

**Step 1:** List a few multiples of 6 (6, 12, 18, 24, 30, . . . ) and 9 (9, 18, 27, 36, . . . . )**Step 2:** The common multiples from the multiples of 6 and 9 are 18, 36, . . .**Step 3:** The smallest common multiple of 6 and 9 is 18.

∴ The least common multiple of 6 and 9 = 18.

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### LCM of 6 and 9 by Prime Factorization

Prime factorization of 6 and 9 is (2 × 3) = 21 × 31 and (3 × 3) = 32 respectively. LCM of 6 and 9 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 21 × 32 = 18.Hence, the LCM of 6 and 9 by prime factorization is 18.

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