Least Common Multiple of 2014 and 2016

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 2014 and 2016 the smallest integer that is 2030112 that is divisible by both numbers.

Least Common Multiple (LCM) of 2014 and 2016 is 2030112.

LCM(2014,2016) = 2030112

LCM of 2014 and 2016

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

LCM of:
and

Least Common Multiple of 2014 and 2016

LCM of 2014 and 2016 is 2030112

Least common multiple can be found by multiplying the highest exponent prime factors of 2014 and 2016. First we will calculate the prime factors of 2014 and 2016.

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

Prime Factorization of 2016


2 2016
2 1008
2 504
2 252
2 126
3 63
3 21
7 7
1

Prime factors of 2016 are 2, 3,7. Prime factorization of 2016 in exponential form is:

2016 = 25×32×71

Now multiplying the highest exponent prime factors to calculate the LCM of 2014 and 2016.

LCM(2014,2016) = 25×32×71×191×531
LCM(2014,2016) = 2030112

Factors of 2014

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

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

Factors of 2016

List of positive integer factors of 2016 that divides 2016 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 32, 36, 42, 48, 56, 63, 72, 84, 96, 112, 126, 144, 168, 224, 252, 288, 336, 504, 672, 1008, 2016

Least Common Multiple of 2014 and 2016 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2014 and 2016, than apply into the LCM equation.

GCF(2014,2016) = 2
LCM(2014,2016) = ( 2014 × 2016) / 2
LCM(2014,2016) = 4060224 / 2
LCM(2014,2016) = 2030112

Properties of LCM 2014 and 2016

(i) The LCM of 2016 and 2014 is associative

LCM of 2014 and 2016 = LCM of 2016 and 2014

Related Least Common Multiples of 2014

Related Least Common Multiples of 2016

Frequently Asked Questions on LCM of 2014 and 2016

1. What is the LCM of 2014 and 2016?

Answer: LCM of 2014 and 2016 is 2030112.

2. 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.

3. What are the Factors of 2016?

Answer: Factors of 2016 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 32, 36, 42, 48, 56, 63, 72, 84, 96, 112, 126, 144, 168, 224, 252, 288, 336, 504, 672, 1008, 2016. There are 36 integers that are factors of 2016. The greatest factor of 2016 is 2016.

4. How to Find the LCM of 2014 and 2016?

Answer:

Least Common Multiple of 2014 and 2016 = 2030112

Step 1: Find the prime factorization of 2014

2014 = 2 x 19 x 53

Step 2: Find the prime factorization of 2016

2016 = 2 x 2 x 2 x 2 x 2 x 3 x 3 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 = 2030112 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 7 x 19 x 53

Step 4: Therefore, the least common multiple of 2014 and 2016 is 2030112.