Least Common Multiple of 10005 and 10013

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

• Least Common Multiple of 10005 and 10013 by Prime method
• Least Common Multiple of 10005 and 10013 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 10005 and 10013. First we will calculate the prime factors of 10005 and 10013.

Prime Factorization of 10005

Prime factors of 10005 are 3, 5, 23,29. Prime factorization of 10005 in exponential form is:

10005 = 3¹×5¹×23¹×29¹

Prime Factorization of 10013

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 10005 and 10013.

LCM(10005,10013) = 3¹×5¹×17¹×19¹×23¹×29¹×31¹
LCM(10005,10013) = 100180065

Factors of 10005

List of positive integer factors of 10005 that divides 10005 without a remainder.

1, 3, 5, 15, 23, 29, 69, 87, 115, 145, 345, 435, 667, 2001, 3335, 10005

Factors of 10013

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

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

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10005 and 10013, than apply into the LCM equation.

GCF(10005,10013) = 1
LCM(10005,10013) = ( 10005 × 10013) / 1
LCM(10005,10013) = 100180065 / 1
LCM(10005,10013) = 100180065

(i) The LCM of 10013 and 10005 is associative

LCM of 10005 and 10013 = LCM of 10013 and 10005

1. What is the LCM of 10005 and 10013?

Answer: LCM of 10005 and 10013 is 100180065.

2. What are the Factors of 10005?

Answer: Factors of 10005 are 1, 3, 5, 15, 23, 29, 69, 87, 115, 145, 345, 435, 667, 2001, 3335, 10005. There are 16 integers that are factors of 10005. The greatest factor of 10005 is 10005.

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 10005 and 10013?

Answer:

Least Common Multiple of 10005 and 10013 = 100180065

Step 1: Find the prime factorization of 10005

10005 = 3 x 5 x 23 x 29

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 = 100180065 = 3 x 5 x 17 x 19 x 23 x 29 x 31

Step 4: Therefore, the least common multiple of 10005 and 10013 is 100180065.