Least Common Multiple of 8004 and 8008

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 8004 and 8008 the smallest integer that is 16024008 that is divisible by both numbers.

Least Common Multiple (LCM) of 8004 and 8008 is 16024008.

LCM(8004,8008) = 16024008

LCM of 8004 and 8008

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

LCM of:
and

Least Common Multiple of 8004 and 8008

LCM of 8004 and 8008 is 16024008

Least common multiple can be found by multiplying the highest exponent prime factors of 8004 and 8008. First we will calculate the prime factors of 8004 and 8008.

Prime Factorization of 8004


2 8004
2 4002
3 2001
23 667
29 29
1

Prime factors of 8004 are 2, 3, 23,29. Prime factorization of 8004 in exponential form is:

8004 = 22×31×231×291

Prime Factorization of 8008


2 8008
2 4004
2 2002
7 1001
11 143
13 13
1

Prime factors of 8008 are 2, 7, 11,13. Prime factorization of 8008 in exponential form is:

8008 = 23×71×111×131

Now multiplying the highest exponent prime factors to calculate the LCM of 8004 and 8008.

LCM(8004,8008) = 23×31×71×111×131×231×291
LCM(8004,8008) = 16024008

Factors of 8004

List of positive integer factors of 8004 that divides 8004 without a remainder.

1, 2, 3, 4, 6, 12, 23, 29, 46, 58, 69, 87, 92, 116, 138, 174, 276, 348, 667, 1334, 2001, 2668, 4002, 8004

Factors of 8008

List of positive integer factors of 8008 that divides 8008 without a remainder.

1, 2, 4, 7, 8, 11, 13, 14, 22, 26, 28, 44, 52, 56, 77, 88, 91, 104, 143, 154, 182, 286, 308, 364, 572, 616, 728, 1001, 1144, 2002, 4004, 8008

Least Common Multiple of 8004 and 8008 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8004 and 8008, than apply into the LCM equation.

GCF(8004,8008) = 4
LCM(8004,8008) = ( 8004 × 8008) / 4
LCM(8004,8008) = 64096032 / 4
LCM(8004,8008) = 16024008

Properties of LCM 8004 and 8008

(i) The LCM of 8008 and 8004 is associative

LCM of 8004 and 8008 = LCM of 8008 and 8004

Related Least Common Multiples of 8004

Related Least Common Multiples of 8008

Frequently Asked Questions on LCM of 8004 and 8008

1. What is the LCM of 8004 and 8008?

Answer: LCM of 8004 and 8008 is 16024008.

2. What are the Factors of 8004?

Answer: Factors of 8004 are 1, 2, 3, 4, 6, 12, 23, 29, 46, 58, 69, 87, 92, 116, 138, 174, 276, 348, 667, 1334, 2001, 2668, 4002, 8004. There are 24 integers that are factors of 8004. The greatest factor of 8004 is 8004.

3. What are the Factors of 8008?

Answer: Factors of 8008 are 1, 2, 4, 7, 8, 11, 13, 14, 22, 26, 28, 44, 52, 56, 77, 88, 91, 104, 143, 154, 182, 286, 308, 364, 572, 616, 728, 1001, 1144, 2002, 4004, 8008. There are 32 integers that are factors of 8008. The greatest factor of 8008 is 8008.

4. How to Find the LCM of 8004 and 8008?

Answer:

Least Common Multiple of 8004 and 8008 = 16024008

Step 1: Find the prime factorization of 8004

8004 = 2 x 2 x 3 x 23 x 29

Step 2: Find the prime factorization of 8008

8008 = 2 x 2 x 2 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 = 16024008 = 2 x 2 x 2 x 3 x 7 x 11 x 13 x 23 x 29

Step 4: Therefore, the least common multiple of 8004 and 8008 is 16024008.