Least Common Multiple of 10005 and 10009

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

• Least Common Multiple of 10005 and 10009 by Prime method
• Least Common Multiple of 10005 and 10009 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 10005 and 10009. First we will calculate the prime factors of 10005 and 10009.

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 10009

Prime factors of 10009 are 10009. Prime factorization of 10009 in exponential form is:

10009 = 10009¹

Now multiplying the highest exponent prime factors to calculate the LCM of 10005 and 10009.

LCM(10005,10009) = 3¹×5¹×23¹×29¹×10009¹
LCM(10005,10009) = 100140045

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 10009

List of positive integer factors of 10009 that divides 10009 without a remainder.

1, 10009

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10005 and 10009, than apply into the LCM equation.

GCF(10005,10009) = 1
LCM(10005,10009) = ( 10005 × 10009) / 1
LCM(10005,10009) = 100140045 / 1
LCM(10005,10009) = 100140045

(i) The LCM of 10009 and 10005 is associative

LCM of 10005 and 10009 = LCM of 10009 and 10005

1. What is the LCM of 10005 and 10009?

Answer: LCM of 10005 and 10009 is 100140045.

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 10009?

Answer: Factors of 10009 are 1, 10009. There are 2 integers that are factors of 10009. The greatest factor of 10009 is 10009.

4. How to Find the LCM of 10005 and 10009?

Answer:

Least Common Multiple of 10005 and 10009 = 100140045

Step 1: Find the prime factorization of 10005

10005 = 3 x 5 x 23 x 29

Step 2: Find the prime factorization of 10009

10009 = 10009

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

LCM = 100140045 = 3 x 5 x 23 x 29 x 10009

Step 4: Therefore, the least common multiple of 10005 and 10009 is 100140045.