Least Common Multiple of 40006 and 40010

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

• Least Common Multiple of 40006 and 40010 by Prime method
• Least Common Multiple of 40006 and 40010 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 40006 and 40010. First we will calculate the prime factors of 40006 and 40010.

Prime Factorization of 40006

Prime factors of 40006 are 2, 83,241. Prime factorization of 40006 in exponential form is:

40006 = 2¹×83¹×241¹

Prime Factorization of 40010

Prime factors of 40010 are 2, 5,4001. Prime factorization of 40010 in exponential form is:

40010 = 2¹×5¹×4001¹

Now multiplying the highest exponent prime factors to calculate the LCM of 40006 and 40010.

LCM(40006,40010) = 2¹×5¹×83¹×241¹×4001¹
LCM(40006,40010) = 800320030

Factors of 40006

List of positive integer factors of 40006 that divides 40006 without a remainder.

1, 2, 83, 166, 241, 482, 20003, 40006

Factors of 40010

List of positive integer factors of 40010 that divides 40010 without a remainder.

1, 2, 5, 10, 4001, 8002, 20005, 40010

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 40006 and 40010, than apply into the LCM equation.

GCF(40006,40010) = 2
LCM(40006,40010) = ( 40006 × 40010) / 2
LCM(40006,40010) = 1600640060 / 2
LCM(40006,40010) = 800320030

(i) The LCM of 40010 and 40006 is associative

LCM of 40006 and 40010 = LCM of 40010 and 40006

1. What is the LCM of 40006 and 40010?

Answer: LCM of 40006 and 40010 is 800320030.

2. What are the Factors of 40006?

Answer: Factors of 40006 are 1, 2, 83, 166, 241, 482, 20003, 40006. There are 8 integers that are factors of 40006. The greatest factor of 40006 is 40006.

3. What are the Factors of 40010?

Answer: Factors of 40010 are 1, 2, 5, 10, 4001, 8002, 20005, 40010. There are 8 integers that are factors of 40010. The greatest factor of 40010 is 40010.

4. How to Find the LCM of 40006 and 40010?

Answer:

Least Common Multiple of 40006 and 40010 = 800320030

Step 1: Find the prime factorization of 40006

40006 = 2 x 83 x 241

Step 2: Find the prime factorization of 40010

40010 = 2 x 5 x 4001

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

LCM = 800320030 = 2 x 5 x 83 x 241 x 4001

Step 4: Therefore, the least common multiple of 40006 and 40010 is 800320030.