Least Common Multiple of 10008 and 10013

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 10008 and 10013 the smallest integer that is 100210104 that is divisible by both numbers.

Least Common Multiple (LCM) of 10008 and 10013 is 100210104.

LCM(10008,10013) = 100210104

LCM of 10008 and 10013

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

LCM of:
and

Least Common Multiple of 10008 and 10013

LCM of 10008 and 10013 is 100210104

Least common multiple can be found by multiplying the highest exponent prime factors of 10008 and 10013. First we will calculate the prime factors of 10008 and 10013.

Prime Factorization of 10008


2 10008
2 5004
2 2502
3 1251
3 417
139 139
1

Prime factors of 10008 are 2, 3,139. Prime factorization of 10008 in exponential form is:

10008 = 23×32×1391

Prime Factorization of 10013


17 10013
19 589
31 31
1

Prime factors of 10013 are 17, 19,31. Prime factorization of 10013 in exponential form is:

10013 = 171×191×311

Now multiplying the highest exponent prime factors to calculate the LCM of 10008 and 10013.

LCM(10008,10013) = 23×32×171×191×311×1391
LCM(10008,10013) = 100210104

Factors of 10008

List of positive integer factors of 10008 that divides 10008 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72, 139, 278, 417, 556, 834, 1112, 1251, 1668, 2502, 3336, 5004, 10008

Factors of 10013

List of positive integer factors of 10013 that divides 10013 without a remainder.

1, 17, 19, 31, 323, 527, 589, 10013

Least Common Multiple of 10008 and 10013 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10008 and 10013, than apply into the LCM equation.

GCF(10008,10013) = 1
LCM(10008,10013) = ( 10008 × 10013) / 1
LCM(10008,10013) = 100210104 / 1
LCM(10008,10013) = 100210104

Properties of LCM 10008 and 10013

(i) The LCM of 10013 and 10008 is associative

LCM of 10008 and 10013 = LCM of 10013 and 10008

Related Least Common Multiples of 10008

Related Least Common Multiples of 10013

Frequently Asked Questions on LCM of 10008 and 10013

1. What is the LCM of 10008 and 10013?

Answer: LCM of 10008 and 10013 is 100210104.

2. What are the Factors of 10008?

Answer: Factors of 10008 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72, 139, 278, 417, 556, 834, 1112, 1251, 1668, 2502, 3336, 5004, 10008. There are 24 integers that are factors of 10008. The greatest factor of 10008 is 10008.

3. What are the Factors of 10013?

Answer: Factors of 10013 are 1, 17, 19, 31, 323, 527, 589, 10013. There are 8 integers that are factors of 10013. The greatest factor of 10013 is 10013.

4. How to Find the LCM of 10008 and 10013?

Answer:

Least Common Multiple of 10008 and 10013 = 100210104

Step 1: Find the prime factorization of 10008

10008 = 2 x 2 x 2 x 3 x 3 x 139

Step 2: Find the prime factorization of 10013

10013 = 17 x 19 x 31

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

LCM = 100210104 = 2 x 2 x 2 x 3 x 3 x 17 x 19 x 31 x 139

Step 4: Therefore, the least common multiple of 10008 and 10013 is 100210104.