Least Common Multiple of 4000 and 4007

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 4000 and 4007 the smallest integer that is 16028000 that is divisible by both numbers.

Least Common Multiple (LCM) of 4000 and 4007 is 16028000.

LCM(4000,4007) = 16028000

LCM of 4000 and 4007

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

LCM of:
and

Least Common Multiple of 4000 and 4007

LCM of 4000 and 4007 is 16028000

Least common multiple can be found by multiplying the highest exponent prime factors of 4000 and 4007. First we will calculate the prime factors of 4000 and 4007.

Prime Factorization of 4000


2 4000
2 2000
2 1000
2 500
2 250
5 125
5 25
5 5
1

Prime factors of 4000 are 2,5. Prime factorization of 4000 in exponential form is:

4000 = 25×53

Prime Factorization of 4007


4007 4007
1

Prime factors of 4007 are 4007. Prime factorization of 4007 in exponential form is:

4007 = 40071

Now multiplying the highest exponent prime factors to calculate the LCM of 4000 and 4007.

LCM(4000,4007) = 25×53×40071
LCM(4000,4007) = 16028000

Factors of 4000

List of positive integer factors of 4000 that divides 4000 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 125, 160, 200, 250, 400, 500, 800, 1000, 2000, 4000

Factors of 4007

List of positive integer factors of 4007 that divides 4007 without a remainder.

1, 4007

Least Common Multiple of 4000 and 4007 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 4000 and 4007, than apply into the LCM equation.

GCF(4000,4007) = 1
LCM(4000,4007) = ( 4000 × 4007) / 1
LCM(4000,4007) = 16028000 / 1
LCM(4000,4007) = 16028000

Properties of LCM 4000 and 4007

(i) The LCM of 4007 and 4000 is associative

LCM of 4000 and 4007 = LCM of 4007 and 4000

Related Least Common Multiples of 4000

Related Least Common Multiples of 4007

Frequently Asked Questions on LCM of 4000 and 4007

1. What is the LCM of 4000 and 4007?

Answer: LCM of 4000 and 4007 is 16028000.

2. What are the Factors of 4000?

Answer: Factors of 4000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 125, 160, 200, 250, 400, 500, 800, 1000, 2000, 4000. There are 24 integers that are factors of 4000. The greatest factor of 4000 is 4000.

3. What are the Factors of 4007?

Answer: Factors of 4007 are 1, 4007. There are 2 integers that are factors of 4007. The greatest factor of 4007 is 4007.

4. How to Find the LCM of 4000 and 4007?

Answer:

Least Common Multiple of 4000 and 4007 = 16028000

Step 1: Find the prime factorization of 4000

4000 = 2 x 2 x 2 x 2 x 2 x 5 x 5 x 5

Step 2: Find the prime factorization of 4007

4007 = 4007

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

LCM = 16028000 = 2 x 2 x 2 x 2 x 2 x 5 x 5 x 5 x 4007

Step 4: Therefore, the least common multiple of 4000 and 4007 is 16028000.