Least Common Multiple of 2007 and 2008

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 2007 and 2008 the smallest integer that is 4030056 that is divisible by both numbers.

Least Common Multiple (LCM) of 2007 and 2008 is 4030056.

LCM(2007,2008) = 4030056

LCM of 2007 and 2008

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

LCM of:
and

Least Common Multiple of 2007 and 2008

LCM of 2007 and 2008 is 4030056

Least common multiple can be found by multiplying the highest exponent prime factors of 2007 and 2008. First we will calculate the prime factors of 2007 and 2008.

Prime Factorization of 2007


3 2007
3 669
223 223
1

Prime factors of 2007 are 3,223. Prime factorization of 2007 in exponential form is:

2007 = 32×2231

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

Now multiplying the highest exponent prime factors to calculate the LCM of 2007 and 2008.

LCM(2007,2008) = 23×32×2231×2511
LCM(2007,2008) = 4030056

Factors of 2007

List of positive integer factors of 2007 that divides 2007 without a remainder.

1, 3, 9, 223, 669, 2007

Factors of 2008

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

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

Least Common Multiple of 2007 and 2008 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2007 and 2008, than apply into the LCM equation.

GCF(2007,2008) = 1
LCM(2007,2008) = ( 2007 × 2008) / 1
LCM(2007,2008) = 4030056 / 1
LCM(2007,2008) = 4030056

Properties of LCM 2007 and 2008

(i) The LCM of 2008 and 2007 is associative

LCM of 2007 and 2008 = LCM of 2008 and 2007

Related Least Common Multiples of 2007

Related Least Common Multiples of 2008

Frequently Asked Questions on LCM of 2007 and 2008

1. What is the LCM of 2007 and 2008?

Answer: LCM of 2007 and 2008 is 4030056.

2. What are the Factors of 2007?

Answer: Factors of 2007 are 1, 3, 9, 223, 669, 2007. There are 6 integers that are factors of 2007. The greatest factor of 2007 is 2007.

3. 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.

4. How to Find the LCM of 2007 and 2008?

Answer:

Least Common Multiple of 2007 and 2008 = 4030056

Step 1: Find the prime factorization of 2007

2007 = 3 x 3 x 223

Step 2: Find the prime factorization of 2008

2008 = 2 x 2 x 2 x 251

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

LCM = 4030056 = 2 x 2 x 2 x 3 x 3 x 223 x 251

Step 4: Therefore, the least common multiple of 2007 and 2008 is 4030056.