Least Common Multiple of 40002 and 40007

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

• Least Common Multiple of 40002 and 40007 by Prime method
• Least Common Multiple of 40002 and 40007 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 40002 and 40007. First we will calculate the prime factors of 40002 and 40007.

Prime Factorization of 40002

Prime factors of 40002 are 2, 3, 59,113. Prime factorization of 40002 in exponential form is:

40002 = 2¹×3¹×59¹×113¹

Prime Factorization of 40007

Prime factors of 40007 are 11,3637. Prime factorization of 40007 in exponential form is:

40007 = 11¹×3637¹

Now multiplying the highest exponent prime factors to calculate the LCM of 40002 and 40007.

LCM(40002,40007) = 2¹×3¹×11¹×59¹×113¹×3637¹
LCM(40002,40007) = 1600360014

Factors of 40002

List of positive integer factors of 40002 that divides 40002 without a remainder.

1, 2, 3, 6, 59, 113, 118, 177, 226, 339, 354, 678, 6667, 13334, 20001, 40002

Factors of 40007

List of positive integer factors of 40007 that divides 40007 without a remainder.

1, 11, 3637, 40007

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 40002 and 40007, than apply into the LCM equation.

GCF(40002,40007) = 1
LCM(40002,40007) = ( 40002 × 40007) / 1
LCM(40002,40007) = 1600360014 / 1
LCM(40002,40007) = 1600360014

(i) The LCM of 40007 and 40002 is associative

LCM of 40002 and 40007 = LCM of 40007 and 40002

1. What is the LCM of 40002 and 40007?

Answer: LCM of 40002 and 40007 is 1600360014.

2. What are the Factors of 40002?

Answer: Factors of 40002 are 1, 2, 3, 6, 59, 113, 118, 177, 226, 339, 354, 678, 6667, 13334, 20001, 40002. There are 16 integers that are factors of 40002. The greatest factor of 40002 is 40002.

3. What are the Factors of 40007?

Answer: Factors of 40007 are 1, 11, 3637, 40007. There are 4 integers that are factors of 40007. The greatest factor of 40007 is 40007.

4. How to Find the LCM of 40002 and 40007?

Answer:

Least Common Multiple of 40002 and 40007 = 1600360014

Step 1: Find the prime factorization of 40002

40002 = 2 x 3 x 59 x 113

Step 2: Find the prime factorization of 40007

40007 = 11 x 3637

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

LCM = 1600360014 = 2 x 3 x 11 x 59 x 113 x 3637

Step 4: Therefore, the least common multiple of 40002 and 40007 is 1600360014.