LCM of 12 and also 14 is the smallest number amongst all common multiples the 12 and 14. The first couple of multiples that 12 and also 14 space (12, 24, 36, 48, 60, 72, 84, . . . ) and (14, 28, 42, 56, 70, 84, . . . ) respectively. There space 3 frequently used techniques to find LCM the 12 and also 14 - by listing multiples, by division method, and by element factorization.

You are watching: Least common multiple of 12 and 14

1.LCM of 12 and also 14
2.List of Methods
3.Solved Examples
4.FAQs

Answer: LCM of 12 and also 14 is 84.

*

Explanation:

The LCM of two non-zero integers, x(12) and also y(14), is the smallest confident integer m(84) the is divisible by both x(12) and y(14) without any remainder.


The methods to discover the LCM that 12 and also 14 are described below.

By department MethodBy prime Factorization MethodBy Listing Multiples

LCM of 12 and also 14 by division Method

*

To calculate the LCM the 12 and 14 by the division method, we will divide the numbers(12, 14) by your prime determinants (preferably common). The product of this divisors gives the LCM that 12 and 14.

Step 3: proceed the steps until just 1s room left in the last row.

The LCM that 12 and also 14 is the product of all prime numbers on the left, i.e. LCM(12, 14) by division method = 2 × 2 × 3 × 7 = 84.

LCM the 12 and also 14 by prime Factorization

Prime administer of 12 and also 14 is (2 × 2 × 3) = 22 × 31 and (2 × 7) = 21 × 71 respectively. LCM that 12 and also 14 can be derived by multiply prime determinants raised to their respective highest power, i.e. 22 × 31 × 71 = 84.Hence, the LCM of 12 and also 14 by element factorization is 84.

LCM the 12 and 14 by Listing Multiples

*

To calculate the LCM the 12 and 14 by listing out the usual multiples, we have the right to follow the given below steps:

Step 1: perform a couple of multiples of 12 (12, 24, 36, 48, 60, 72, 84, . . . ) and 14 (14, 28, 42, 56, 70, 84, . . . . )Step 2: The typical multiples indigenous the multiples that 12 and also 14 space 84, 168, . . .Step 3: The smallest usual multiple the 12 and also 14 is 84.

∴ The least usual multiple the 12 and also 14 = 84.

☛ also Check:


*


FAQs ~ above LCM that 12 and 14

What is the LCM the 12 and 14?

The LCM that 12 and 14 is 84. To uncover the LCM the 12 and also 14, we need to discover the multiples of 12 and 14 (multiples of 12 = 12, 24, 36, 48 . . . . 84; multiples of 14 = 14, 28, 42, 56 . . . . 84) and choose the the smallest multiple that is precisely divisible by 12 and 14, i.e., 84.

If the LCM of 14 and also 12 is 84, find its GCF.

LCM(14, 12) × GCF(14, 12) = 14 × 12Since the LCM that 14 and 12 = 84⇒ 84 × GCF(14, 12) = 168Therefore, the greatest typical factor (GCF) = 168/84 = 2.

How to discover the LCM that 12 and also 14 by element Factorization?

To uncover the LCM the 12 and 14 making use of prime factorization, us will uncover the element factors, (12 = 2 × 2 × 3) and also (14 = 2 × 7). LCM the 12 and 14 is the product of prime components raised to your respective greatest exponent among the numbers 12 and 14.⇒ LCM of 12, 14 = 22 × 31 × 71 = 84.

What is the Relation in between GCF and also LCM that 12, 14?

The following equation can be provided to refer the relation in between GCF and LCM the 12 and 14, i.e. GCF × LCM = 12 × 14.

See more: What Color Does Blue And Red Make Purple ? Creating Different Shades Of Purple

What is the the very least Perfect Square Divisible through 12 and 14?

The least number divisible through 12 and also 14 = LCM(12, 14)LCM that 12 and 14 = 2 × 2 × 3 × 7 ⇒ the very least perfect square divisible by every 12 and 14 = LCM(12, 14) × 3 × 7 = 1764 Therefore, 1764 is the forced number.