Least Common Multiple of 4000 and 4008

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 4008 the smallest integer that is 2004000 that is divisible by both numbers.

Least Common Multiple (LCM) of 4000 and 4008 is 2004000.

LCM(4000,4008) = 2004000

LCM of 4000 and 4008

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

LCM of:
and

Least Common Multiple of 4000 and 4008

LCM of 4000 and 4008 is 2004000

Least common multiple can be found by multiplying the highest exponent prime factors of 4000 and 4008. First we will calculate the prime factors of 4000 and 4008.

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 4008


2 4008
2 2004
2 1002
3 501
167 167
1

Prime factors of 4008 are 2, 3,167. Prime factorization of 4008 in exponential form is:

4008 = 23×31×1671

Now multiplying the highest exponent prime factors to calculate the LCM of 4000 and 4008.

LCM(4000,4008) = 25×31×53×1671
LCM(4000,4008) = 2004000

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 4008

List of positive integer factors of 4008 that divides 4008 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 167, 334, 501, 668, 1002, 1336, 2004, 4008

Least Common Multiple of 4000 and 4008 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 4008, than apply into the LCM equation.

GCF(4000,4008) = 8
LCM(4000,4008) = ( 4000 × 4008) / 8
LCM(4000,4008) = 16032000 / 8
LCM(4000,4008) = 2004000

Properties of LCM 4000 and 4008

(i) The LCM of 4008 and 4000 is associative

LCM of 4000 and 4008 = LCM of 4008 and 4000

Related Least Common Multiples of 4000

Related Least Common Multiples of 4008

Frequently Asked Questions on LCM of 4000 and 4008

1. What is the LCM of 4000 and 4008?

Answer: LCM of 4000 and 4008 is 2004000.

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 4008?

Answer: Factors of 4008 are 1, 2, 3, 4, 6, 8, 12, 24, 167, 334, 501, 668, 1002, 1336, 2004, 4008. There are 16 integers that are factors of 4008. The greatest factor of 4008 is 4008.

4. How to Find the LCM of 4000 and 4008?

Answer:

Least Common Multiple of 4000 and 4008 = 2004000

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 4008

4008 = 2 x 2 x 2 x 3 x 167

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

LCM = 2004000 = 2 x 2 x 2 x 2 x 2 x 3 x 5 x 5 x 5 x 167

Step 4: Therefore, the least common multiple of 4000 and 4008 is 2004000.