Least Common Multiple of 10002 and 10005

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

• Least Common Multiple of 10002 and 10005 by Prime method
• Least Common Multiple of 10002 and 10005 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 10002 and 10005. First we will calculate the prime factors of 10002 and 10005.

Prime Factorization of 10002

Prime factors of 10002 are 2, 3,1667. Prime factorization of 10002 in exponential form is:

10002 = 2¹×3¹×1667¹

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

Now multiplying the highest exponent prime factors to calculate the LCM of 10002 and 10005.

LCM(10002,10005) = 2¹×3¹×5¹×23¹×29¹×1667¹
LCM(10002,10005) = 33356670

Factors of 10002

List of positive integer factors of 10002 that divides 10002 without a remainder.

1, 2, 3, 6, 1667, 3334, 5001, 10002

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

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10002 and 10005, than apply into the LCM equation.

GCF(10002,10005) = 3
LCM(10002,10005) = ( 10002 × 10005) / 3
LCM(10002,10005) = 100070010 / 3
LCM(10002,10005) = 33356670

(i) The LCM of 10005 and 10002 is associative

LCM of 10002 and 10005 = LCM of 10005 and 10002

1. What is the LCM of 10002 and 10005?

Answer: LCM of 10002 and 10005 is 33356670.

2. What are the Factors of 10002?

Answer: Factors of 10002 are 1, 2, 3, 6, 1667, 3334, 5001, 10002. There are 8 integers that are factors of 10002. The greatest factor of 10002 is 10002.

3. 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.

4. How to Find the LCM of 10002 and 10005?

Answer:

Least Common Multiple of 10002 and 10005 = 33356670

Step 1: Find the prime factorization of 10002

10002 = 2 x 3 x 1667

Step 2: Find the prime factorization of 10005

10005 = 3 x 5 x 23 x 29

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

LCM = 33356670 = 2 x 3 x 5 x 23 x 29 x 1667

Step 4: Therefore, the least common multiple of 10002 and 10005 is 33356670.