Least Common Multiple of 2007 and 2013

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 2013 the smallest integer that is 1346697 that is divisible by both numbers.

Least Common Multiple (LCM) of 2007 and 2013 is 1346697.

LCM(2007,2013) = 1346697

LCM of 2007 and 2013

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

LCM of:
and

Least Common Multiple of 2007 and 2013

LCM of 2007 and 2013 is 1346697

Least common multiple can be found by multiplying the highest exponent prime factors of 2007 and 2013. First we will calculate the prime factors of 2007 and 2013.

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 2013


3 2013
11 671
61 61
1

Prime factors of 2013 are 3, 11,61. Prime factorization of 2013 in exponential form is:

2013 = 31×111×611

Now multiplying the highest exponent prime factors to calculate the LCM of 2007 and 2013.

LCM(2007,2013) = 32×111×611×2231
LCM(2007,2013) = 1346697

Factors of 2007

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

1, 3, 9, 223, 669, 2007

Factors of 2013

List of positive integer factors of 2013 that divides 2013 without a remainder.

1, 3, 11, 33, 61, 183, 671, 2013

Least Common Multiple of 2007 and 2013 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 2013, than apply into the LCM equation.

GCF(2007,2013) = 3
LCM(2007,2013) = ( 2007 × 2013) / 3
LCM(2007,2013) = 4040091 / 3
LCM(2007,2013) = 1346697

Properties of LCM 2007 and 2013

(i) The LCM of 2013 and 2007 is associative

LCM of 2007 and 2013 = LCM of 2013 and 2007

Related Least Common Multiples of 2007

Related Least Common Multiples of 2013

Frequently Asked Questions on LCM of 2007 and 2013

1. What is the LCM of 2007 and 2013?

Answer: LCM of 2007 and 2013 is 1346697.

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 2013?

Answer: Factors of 2013 are 1, 3, 11, 33, 61, 183, 671, 2013. There are 8 integers that are factors of 2013. The greatest factor of 2013 is 2013.

4. How to Find the LCM of 2007 and 2013?

Answer:

Least Common Multiple of 2007 and 2013 = 1346697

Step 1: Find the prime factorization of 2007

2007 = 3 x 3 x 223

Step 2: Find the prime factorization of 2013

2013 = 3 x 11 x 61

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

LCM = 1346697 = 3 x 3 x 11 x 61 x 223

Step 4: Therefore, the least common multiple of 2007 and 2013 is 1346697.