Least Common Multiple of 2008 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 2008 and 2016 the smallest integer that is 506016 that is divisible by both numbers.

Least Common Multiple (LCM) of 2008 and 2016 is 506016.

LCM(2008,2016) = 506016

LCM of 2008 and 2016

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

LCM of:
and

Least Common Multiple of 2008 and 2016

LCM of 2008 and 2016 is 506016

Least common multiple can be found by multiplying the highest exponent prime factors of 2008 and 2016. First we will calculate the prime factors of 2008 and 2016.

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 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 2008 and 2016.

LCM(2008,2016) = 25×32×71×2511
LCM(2008,2016) = 506016

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 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 2008 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 2008 and 2016, than apply into the LCM equation.

GCF(2008,2016) = 8
LCM(2008,2016) = ( 2008 × 2016) / 8
LCM(2008,2016) = 4048128 / 8
LCM(2008,2016) = 506016

Properties of LCM 2008 and 2016

(i) The LCM of 2016 and 2008 is associative

LCM of 2008 and 2016 = LCM of 2016 and 2008

Related Least Common Multiples of 2008

Related Least Common Multiples of 2016

Frequently Asked Questions on LCM of 2008 and 2016

1. What is the LCM of 2008 and 2016?

Answer: LCM of 2008 and 2016 is 506016.

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 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 2008 and 2016?

Answer:

Least Common Multiple of 2008 and 2016 = 506016

Step 1: Find the prime factorization of 2008

2008 = 2 x 2 x 2 x 251

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 = 506016 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 7 x 251

Step 4: Therefore, the least common multiple of 2008 and 2016 is 506016.