Least Common Multiple of 2008 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 2008 and 2014 the smallest integer that is 2022056 that is divisible by both numbers.

Least Common Multiple (LCM) of 2008 and 2014 is 2022056.

LCM(2008,2014) = 2022056

LCM of 2008 and 2014

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

LCM of:
and

Least Common Multiple of 2008 and 2014

LCM of 2008 and 2014 is 2022056

Least common multiple can be found by multiplying the highest exponent prime factors of 2008 and 2014. First we will calculate the prime factors of 2008 and 2014.

Prime Factorization of 2008


2 2008
2 1004
2 502
251 251
1

Prime factors of 2008 are 2,251. Prime factorization of 2008 in exponential form is:

2008 = 23×2511

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 2008 and 2014.

LCM(2008,2014) = 23×191×531×2511
LCM(2008,2014) = 2022056

Factors of 2008

List of positive integer factors of 2008 that divides 2008 without a remainder.

1, 2, 4, 8, 251, 502, 1004, 2008

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 2008 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 2008 and 2014, than apply into the LCM equation.

GCF(2008,2014) = 2
LCM(2008,2014) = ( 2008 × 2014) / 2
LCM(2008,2014) = 4044112 / 2
LCM(2008,2014) = 2022056

Properties of LCM 2008 and 2014

(i) The LCM of 2014 and 2008 is associative

LCM of 2008 and 2014 = LCM of 2014 and 2008

Related Least Common Multiples of 2008

Related Least Common Multiples of 2014

Frequently Asked Questions on LCM of 2008 and 2014

1. What is the LCM of 2008 and 2014?

Answer: LCM of 2008 and 2014 is 2022056.

2. What are the Factors of 2008?

Answer: Factors of 2008 are 1, 2, 4, 8, 251, 502, 1004, 2008. There are 8 integers that are factors of 2008. The greatest factor of 2008 is 2008.

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 2008 and 2014?

Answer:

Least Common Multiple of 2008 and 2014 = 2022056

Step 1: Find the prime factorization of 2008

2008 = 2 x 2 x 2 x 251

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 = 2022056 = 2 x 2 x 2 x 19 x 53 x 251

Step 4: Therefore, the least common multiple of 2008 and 2014 is 2022056.