LCM that 12 and also 21 is the the smallest number among all common multiples of 12 and 21. The first few multiples of 12 and 21 room (12, 24, 36, 48, . . . ) and (21, 42, 63, 84, 105, . . . ) respectively. There are 3 generally used techniques to discover LCM of 12 and also 21 - by division method, by listing multiples, and also by prime factorization.

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1. | LCM that 12 and 21 |

2. | List the Methods |

3. | Solved Examples |

4. | FAQs |

**Answer:** LCM of 12 and 21 is 84.

**Explanation: **

The LCM of 2 non-zero integers, x(12) and also y(21), is the smallest hopeful integer m(84) that is divisible through both x(12) and y(21) without any type of remainder.

Let's look in ~ the various methods for finding the LCM the 12 and also 21.

By department MethodBy prime Factorization MethodBy Listing Multiples### LCM that 12 and also 21 by division Method

To calculate the LCM that 12 and 21 through the department method, we will divide the numbers(12, 21) by your prime components (preferably common). The product of these divisors offers the LCM the 12 and 21.

**Step 3:**proceed the procedures until just 1s space left in the last row.

The LCM of 12 and 21 is the product of every prime numbers on the left, i.e. LCM(12, 21) by department method = 2 × 2 × 3 × 7 = 84.

### LCM the 12 and 21 by prime Factorization

Prime administer of 12 and also 21 is (2 × 2 × 3) = 22 × 31 and (3 × 7) = 31 × 71 respectively. LCM of 12 and 21 can be derived by multiply prime components raised to your respective greatest power, i.e. 22 × 31 × 71 = 84.Hence, the LCM that 12 and 21 by element factorization is 84.

### LCM the 12 and also 21 through Listing Multiples

To calculation the LCM of 12 and 21 by listing out the common multiples, we can follow the given below steps:

**Step 1:**perform a few multiples the 12 (12, 24, 36, 48, . . . ) and 21 (21, 42, 63, 84, 105, . . . . )

**Step 2:**The common multiples from the multiples that 12 and also 21 space 84, 168, . . .

**Step 3:**The smallest typical multiple that 12 and also 21 is 84.

∴ The least typical multiple of 12 and also 21 = 84.

**☛ also Check:**

## FAQs ~ above LCM that 12 and 21

### What is the LCM the 12 and 21?

The **LCM the 12 and 21 is 84**. To discover the LCM (least usual multiple) the 12 and 21, we require to find the multiples of 12 and 21 (multiples of 12 = 12, 24, 36, 48 . . . . 84; multiples that 21 = 21, 42, 63, 84) and also choose the smallest multiple that is exactly divisible by 12 and 21, i.e., 84.

### How to uncover the LCM of 12 and also 21 by element Factorization?

To uncover the LCM that 12 and also 21 making use of prime factorization, we will uncover the element factors, (12 = 2 × 2 × 3) and also (21 = 3 × 7). LCM of 12 and also 21 is the product that prime determinants raised to your respective highest exponent amongst the numbers 12 and also 21.⇒ LCM the 12, 21 = 22 × 31 × 71 = 84.

### If the LCM the 21 and 12 is 84, uncover its GCF.

LCM(21, 12) × GCF(21, 12) = 21 × 12Since the LCM that 21 and also 12 = 84⇒ 84 × GCF(21, 12) = 252Therefore, the GCF (greatest common factor) = 252/84 = 3.

### Which the the complying with is the LCM the 12 and 21? 21, 12, 36, 84

The value of LCM of 12, 21 is the smallest typical multiple of 12 and also 21. The number solve the given condition is 84.

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### What is the Relation in between GCF and also LCM that 12, 21?

The adhering to equation have the right to be provided to express the relation in between GCF and also LCM of 12 and also 21, i.e. GCF × LCM = 12 × 21.