Least Common Multiple of 7998 and 8004

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 7998 and 8004 the smallest integer that is 10669332 that is divisible by both numbers.

Least Common Multiple (LCM) of 7998 and 8004 is 10669332.

LCM(7998,8004) = 10669332

LCM of 7998 and 8004

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

LCM of:
and

Least Common Multiple of 7998 and 8004

LCM of 7998 and 8004 is 10669332

Least common multiple can be found by multiplying the highest exponent prime factors of 7998 and 8004. First we will calculate the prime factors of 7998 and 8004.

Prime Factorization of 7998


2 7998
3 3999
31 1333
43 43
1

Prime factors of 7998 are 2, 3, 31,43. Prime factorization of 7998 in exponential form is:

7998 = 21×31×311×431

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

Now multiplying the highest exponent prime factors to calculate the LCM of 7998 and 8004.

LCM(7998,8004) = 22×31×231×291×311×431
LCM(7998,8004) = 10669332

Factors of 7998

List of positive integer factors of 7998 that divides 7998 without a remainder.

1, 2, 3, 6, 31, 43, 62, 86, 93, 129, 186, 258, 1333, 2666, 3999, 7998

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

Least Common Multiple of 7998 and 8004 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7998 and 8004, than apply into the LCM equation.

GCF(7998,8004) = 6
LCM(7998,8004) = ( 7998 × 8004) / 6
LCM(7998,8004) = 64015992 / 6
LCM(7998,8004) = 10669332

Properties of LCM 7998 and 8004

(i) The LCM of 8004 and 7998 is associative

LCM of 7998 and 8004 = LCM of 8004 and 7998

Related Least Common Multiples of 7998

Related Least Common Multiples of 8004

Frequently Asked Questions on LCM of 7998 and 8004

1. What is the LCM of 7998 and 8004?

Answer: LCM of 7998 and 8004 is 10669332.

2. What are the Factors of 7998?

Answer: Factors of 7998 are 1, 2, 3, 6, 31, 43, 62, 86, 93, 129, 186, 258, 1333, 2666, 3999, 7998. There are 16 integers that are factors of 7998. The greatest factor of 7998 is 7998.

3. 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.

4. How to Find the LCM of 7998 and 8004?

Answer:

Least Common Multiple of 7998 and 8004 = 10669332

Step 1: Find the prime factorization of 7998

7998 = 2 x 3 x 31 x 43

Step 2: Find the prime factorization of 8004

8004 = 2 x 2 x 3 x 23 x 29

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

LCM = 10669332 = 2 x 2 x 3 x 23 x 29 x 31 x 43

Step 4: Therefore, the least common multiple of 7998 and 8004 is 10669332.