Least Common Multiple of 10007 and 10010

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

• Least Common Multiple of 10007 and 10010 by Prime method
• Least Common Multiple of 10007 and 10010 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 10007 and 10010. First we will calculate the prime factors of 10007 and 10010.

Prime Factorization of 10007

Prime factors of 10007 are 10007. Prime factorization of 10007 in exponential form is:

10007 = 10007¹

Prime Factorization of 10010

Prime factors of 10010 are 2, 5, 7, 11,13. Prime factorization of 10010 in exponential form is:

10010 = 2¹×5¹×7¹×11¹×13¹

Now multiplying the highest exponent prime factors to calculate the LCM of 10007 and 10010.

LCM(10007,10010) = 2¹×5¹×7¹×11¹×13¹×10007¹
LCM(10007,10010) = 100170070

Factors of 10007

List of positive integer factors of 10007 that divides 10007 without a remainder.

1, 10007

Factors of 10010

List of positive integer factors of 10010 that divides 10010 without a remainder.

1, 2, 5, 7, 10, 11, 13, 14, 22, 26, 35, 55, 65, 70, 77, 91, 110, 130, 143, 154, 182, 286, 385, 455, 715, 770, 910, 1001, 1430, 2002, 5005, 10010

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10007 and 10010, than apply into the LCM equation.

GCF(10007,10010) = 1
LCM(10007,10010) = ( 10007 × 10010) / 1
LCM(10007,10010) = 100170070 / 1
LCM(10007,10010) = 100170070

(i) The LCM of 10010 and 10007 is associative

LCM of 10007 and 10010 = LCM of 10010 and 10007

1. What is the LCM of 10007 and 10010?

Answer: LCM of 10007 and 10010 is 100170070.

2. What are the Factors of 10007?

Answer: Factors of 10007 are 1, 10007. There are 2 integers that are factors of 10007. The greatest factor of 10007 is 10007.

3. What are the Factors of 10010?

Answer: Factors of 10010 are 1, 2, 5, 7, 10, 11, 13, 14, 22, 26, 35, 55, 65, 70, 77, 91, 110, 130, 143, 154, 182, 286, 385, 455, 715, 770, 910, 1001, 1430, 2002, 5005, 10010. There are 32 integers that are factors of 10010. The greatest factor of 10010 is 10010.

4. How to Find the LCM of 10007 and 10010?

Answer:

Least Common Multiple of 10007 and 10010 = 100170070

Step 1: Find the prime factorization of 10007

10007 = 10007

Step 2: Find the prime factorization of 10010

10010 = 2 x 5 x 7 x 11 x 13

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

LCM = 100170070 = 2 x 5 x 7 x 11 x 13 x 10007

Step 4: Therefore, the least common multiple of 10007 and 10010 is 100170070.