LCM of 7 and 12 is the smallest number among all common multiples of 7 and 12. The first few multiples of 7 and 12 are (7, 14, 21, 28, . . . ) and (12, 24, 36, 48, 60, 72, 84, . . . ) respectively. There are 3 commonly used methods to find LCM of 7 and 12 – by listing multiples, by division method, and by prime factorization.

You are watching: Least common multiple of 7 and 12

1. | LCM of 7 and 12 |

2. | List of Methods |

3. | Solved Examples |

4. | FAQs |

**Answer:** LCM of 7 and 12 is 84.

**Explanation: **

The LCM of two non-zero integers, x(7) and y(12), is the smallest positive integer m(84) that is divisible by both x(7) and y(12) without any remainder.

Let's look at the different methods for finding the LCM of 7 and 12.

By Division MethodBy Prime Factorization MethodBy Listing Multiples

### LCM of 7 and 12 by Division Method

To calculate the LCM of 7 and 12 by the division method, we will divide the numbers(7, 12) by their prime factors (preferably common). The product of these divisors gives the LCM of 7 and 12.

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

The LCM of 7 and 12 is the product of all prime numbers on the left, i.e. LCM(7, 12) by division method = 2 × 2 × 3 × 7 = 84.

See more: Have You Ever Needed Someone So Bad Lyrics, Def Leppard

### LCM of 7 and 12 by Prime Factorization

Prime factorization of 7 and 12 is (7) = 71 and (2 × 2 × 3) = 22 × 31 respectively. LCM of 7 and 12 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 22 × 31 × 71 = 84.Hence, the LCM of 7 and 12 by prime factorization is 84.

### LCM of 7 and 12 by Listing Multiples

To calculate the LCM of 7 and 12 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 12 (12, 24, 36, 48, 60, 72, 84, . . . . )**Step 2:** The common multiples from the multiples of 7 and 12 are 84, 168, . . .**Step 3:** The smallest common multiple of 7 and 12 is 84.

∴ The least common multiple of 7 and 12 = 84.

**☛ Also Check:**

## FAQs on LCM of 7 and 12

### What is the LCM of 7 and 12?

The **LCM of 7 and 12 is 84**. To find the least common multiple (LCM) of 7 and 12, we need to find the multiples of 7 and 12 (multiples of 7 = 7, 14, 21, 28 . . . . 84; multiples of 12 = 12, 24, 36, 48 . . . . 84) and choose the smallest multiple that is exactly divisible by 7 and 12, i.e., 84.

### How to Find the LCM of 7 and 12 by Prime Factorization?

To find the LCM of 7 and 12 using prime factorization, we will find the prime factors, (7 = 7) and (12 = 2 × 2 × 3). LCM of 7 and 12 is the product of prime factors raised to their respective highest exponent among the numbers 7 and 12.⇒ LCM of 7, 12 = 22 × 31 × 71 = 84.

### What is the Relation Between GCF and LCM of 7, 12?

The following equation can be used to express the relation between GCF and LCM of 7 and 12, i.e. GCF × LCM = 7 × 12.

### Which of the following is the LCM of 7 and 12? 21, 12, 84, 42

The value of LCM of 7, 12 is the smallest common multiple of 7 and 12. The number satisfying the given condition is 84.

### If the LCM of 12 and 7 is 84, Find its GCF.

See more: Us History Unit 4, Quiz 1: The Issues That Caused Sectionalism To Develop Were ?

LCM(12, 7) × GCF(12, 7) = 12 × 7Since the LCM of 12 and 7 = 84⇒ 84 × GCF(12, 7) = 84Therefore, the GCF = 84/84 = 1.