Least Common Multiple of 12 and 14

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 12 and 14 the smallest integer that is 84 that is divisible by both numbers.

Least Common Multiple (LCM) of 12 and 14 is 84.

LCM(12,14) = 84

LCM of 12 and 14

Least common multiple or lowest common denominator (LCD) can be calculated in three ways;

LCM of:
and

Least Common Multiple of 12 and 14

LCM of 12 and 14 is 84

Least common multiple can be found by multiplying the highest exponent prime factors of 12 and 14. First we will calculate the prime factors of 12 and 14.

Prime Factorization of 12


2 12
2 6
3 3
1

Prime factors of 12 are 2,3. Prime factorization of 12 in exponential form is:

12 = 22×31

Prime Factorization of 14


2 14
7 7
1

Prime factors of 14 are 2,7. Prime factorization of 14 in exponential form is:

14 = 21×71

Now multiplying the highest exponent prime factors to calculate the LCM of 12 and 14.

LCM(12,14) = 22×31×71
LCM(12,14) = 84

Factors of 12

List of positive integer factors of 12 that divides 12 without a remainder.

1, 2, 3, 4, 6, 12

Factors of 14

List of positive integer factors of 14 that divides 14 without a remainder.

1, 2, 7, 14

Least Common Multiple of 12 and 14 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12 and 14, than apply into the LCM equation.

GCF(12,14) = 2
LCM(12,14) = ( 12 × 14) / 2
LCM(12,14) = 168 / 2
LCM(12,14) = 84

Properties of LCM 12 and 14

(i) The LCM of 14 and 12 is associative

LCM of 12 and 14 = LCM of 14 and 12

Related Least Common Multiples of 12

Related Least Common Multiples of 14

Frequently Asked Questions on LCM of 12 and 14

1. What is the LCM of 12 and 14?

Answer: LCM of 12 and 14 is 84.

2. What are the Factors of 12?

Answer: Factors of 12 are 1, 2, 3, 4, 6, 12. There are 6 integers that are factors of 12. The greatest factor of 12 is 12.

3. What are the Factors of 14?

Answer: Factors of 14 are 1, 2, 7, 14. There are 4 integers that are factors of 14. The greatest factor of 14 is 14.

4. How to Find the LCM of 12 and 14?

Answer:

Least Common Multiple of 12 and 14 = 84

Step 1: Find the prime factorization of 12

12 = 2 x 2 x 3

Step 2: Find the prime factorization of 14

14 = 2 x 7

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 84 = 2 x 2 x 3 x 7

Step 4: Therefore, the least common multiple of 12 and 14 is 84.