Least Common Multiple of 2012 and 2014

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 2012 and 2014 the smallest integer that is 2026084 that is divisible by both numbers.

Least Common Multiple (LCM) of 2012 and 2014 is 2026084.

LCM(2012,2014) = 2026084

LCM of 2012 and 2014

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

LCM of:
and

Least Common Multiple of 2012 and 2014

LCM of 2012 and 2014 is 2026084

Least common multiple can be found by multiplying the highest exponent prime factors of 2012 and 2014. First we will calculate the prime factors of 2012 and 2014.

Prime Factorization of 2012


2 2012
2 1006
503 503
1

Prime factors of 2012 are 2,503. Prime factorization of 2012 in exponential form is:

2012 = 22×5031

Prime Factorization of 2014


2 2014
19 1007
53 53
1

Prime factors of 2014 are 2, 19,53. Prime factorization of 2014 in exponential form is:

2014 = 21×191×531

Now multiplying the highest exponent prime factors to calculate the LCM of 2012 and 2014.

LCM(2012,2014) = 22×191×531×5031
LCM(2012,2014) = 2026084

Factors of 2012

List of positive integer factors of 2012 that divides 2012 without a remainder.

1, 2, 4, 503, 1006, 2012

Factors of 2014

List of positive integer factors of 2014 that divides 2014 without a remainder.

1, 2, 19, 38, 53, 106, 1007, 2014

Least Common Multiple of 2012 and 2014 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2012 and 2014, than apply into the LCM equation.

GCF(2012,2014) = 2
LCM(2012,2014) = ( 2012 × 2014) / 2
LCM(2012,2014) = 4052168 / 2
LCM(2012,2014) = 2026084

Properties of LCM 2012 and 2014

(i) The LCM of 2014 and 2012 is associative

LCM of 2012 and 2014 = LCM of 2014 and 2012

Related Least Common Multiples of 2012

Related Least Common Multiples of 2014

Frequently Asked Questions on LCM of 2012 and 2014

1. What is the LCM of 2012 and 2014?

Answer: LCM of 2012 and 2014 is 2026084.

2. What are the Factors of 2012?

Answer: Factors of 2012 are 1, 2, 4, 503, 1006, 2012. There are 6 integers that are factors of 2012. The greatest factor of 2012 is 2012.

3. What are the Factors of 2014?

Answer: Factors of 2014 are 1, 2, 19, 38, 53, 106, 1007, 2014. There are 8 integers that are factors of 2014. The greatest factor of 2014 is 2014.

4. How to Find the LCM of 2012 and 2014?

Answer:

Least Common Multiple of 2012 and 2014 = 2026084

Step 1: Find the prime factorization of 2012

2012 = 2 x 2 x 503

Step 2: Find the prime factorization of 2014

2014 = 2 x 19 x 53

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

LCM = 2026084 = 2 x 2 x 19 x 53 x 503

Step 4: Therefore, the least common multiple of 2012 and 2014 is 2026084.