LCM of 7 and 11 is the smallest number among all common multiples of 7 and 11. The first few multiples of 7 and 11 are (7, 14, 21, 28, . . . ) and (11, 22, 33, 44, 55, 66, . . . ) respectively. There are 3 commonly used methods to find LCM of 7 and 11 – by prime factorization, by division method, and by listing multiples.

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1. | LCM of 7 and 11 |

2. | List of Methods |

3. | Solved Examples |

4. | FAQs |

**Answer:** LCM of 7 and 11 is 77.

**Explanation: **

The LCM of two non-zero integers, x(7) and y(11), is the smallest positive integer m(77) that is divisible by both x(7) and y(11) without any remainder.

The methods to find the LCM of 7 and 11 are explained below.

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By Listing MultiplesBy Prime Factorization MethodBy Division Method

### LCM of 7 and 11 by Listing Multiples

To calculate the LCM of 7 and 11 by listing out the common multiples, we can follow the given below steps:

**Step 1:** List a few multiples of 7 (7, 14, 21, 28, . . . ) and 11 (11, 22, 33, 44, 55, 66, . . . . )**Step 2:** The common multiples from the multiples of 7 and 11 are 77, 154, . . .**Step 3:** The smallest common multiple of 7 and 11 is 77.

∴ The least common multiple of 7 and 11 = 77.

### LCM of 7 and 11 by Prime Factorization

Prime factorization of 7 and 11 is (7) = 71 and (11) = 111 respectively. LCM of 7 and 11 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 71 × 111 = 77.Hence, the LCM of 7 and 11 by prime factorization is 77.

### LCM of 7 and 11 by Division Method

To calculate the LCM of 7 and 11 by the division method, we will divide the numbers(7, 11) by their prime factors (preferably common). The product of these divisors gives the LCM of 7 and 11.

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

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The LCM of 7 and 11 is the product of all prime numbers on the left, i.e. LCM(7, 11) by division method = 7 × 11 = 77.