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

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1. | LCM of 12 and 21 |

2. | List of Methods |

3. | Solved Examples |

4. | FAQs |

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

**Explanation: **

The LCM of two non-zero integers, x(12) and y(21), is the smallest positive integer m(84) that is divisible by both x(12) and y(21) without any remainder.

Let's look at the different methods for finding the LCM of 12 and 21.

By Division MethodBy Prime Factorization MethodBy Listing Multiples### LCM of 12 and 21 by Division Method

To calculate the LCM of 12 and 21 by the division method, we will divide the numbers(12, 21) by their prime factors (preferably common). The product of these divisors gives the LCM of 12 and 21.

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

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

### LCM of 12 and 21 by Prime Factorization

Prime factorization of 12 and 21 is (2 × 2 × 3) = 22 × 31 and (3 × 7) = 31 × 71 respectively. LCM of 12 and 21 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 22 × 31 × 71 = 84.Hence, the LCM of 12 and 21 by prime factorization is 84.

### LCM of 12 and 21 by Listing Multiples

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

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

**Step 2:**The common multiples from the multiples of 12 and 21 are 84, 168, . . .

**Step 3:**The smallest common multiple of 12 and 21 is 84.

∴ The least common multiple of 12 and 21 = 84.

**☛ Also Check:**

## FAQs on LCM of 12 and 21

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

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

### How to Find the LCM of 12 and 21 by Prime Factorization?

To find the LCM of 12 and 21 using prime factorization, we will find the prime factors, (12 = 2 × 2 × 3) and (21 = 3 × 7). LCM of 12 and 21 is the product of prime factors raised to their respective highest exponent among the numbers 12 and 21.⇒ LCM of 12, 21 = 22 × 31 × 71 = 84.

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

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

### Which of the following is the LCM of 12 and 21? 21, 12, 36, 84

The value of LCM of 12, 21 is the smallest common multiple of 12 and 21. The number satisfying the given condition is 84.

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### What is the Relation Between GCF and LCM of 12, 21?

The following equation can be used to express the relation between GCF and LCM of 12 and 21, i.e. GCF × LCM = 12 × 21.