Least Common Multiple of 3998 and 4004

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 3998 and 4004 the smallest integer that is 8003996 that is divisible by both numbers.

Least Common Multiple (LCM) of 3998 and 4004 is 8003996.

LCM(3998,4004) = 8003996

LCM of 3998 and 4004

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

LCM of:
and

Least Common Multiple of 3998 and 4004

LCM of 3998 and 4004 is 8003996

Least common multiple can be found by multiplying the highest exponent prime factors of 3998 and 4004. First we will calculate the prime factors of 3998 and 4004.

Prime Factorization of 3998


2 3998
1999 1999
1

Prime factors of 3998 are 2,1999. Prime factorization of 3998 in exponential form is:

3998 = 21×19991

Prime Factorization of 4004


2 4004
2 2002
7 1001
11 143
13 13
1

Prime factors of 4004 are 2, 7, 11,13. Prime factorization of 4004 in exponential form is:

4004 = 22×71×111×131

Now multiplying the highest exponent prime factors to calculate the LCM of 3998 and 4004.

LCM(3998,4004) = 22×71×111×131×19991
LCM(3998,4004) = 8003996

Factors of 3998

List of positive integer factors of 3998 that divides 3998 without a remainder.

1, 2, 1999, 3998

Factors of 4004

List of positive integer factors of 4004 that divides 4004 without a remainder.

1, 2, 4, 7, 11, 13, 14, 22, 26, 28, 44, 52, 77, 91, 143, 154, 182, 286, 308, 364, 572, 1001, 2002, 4004

Least Common Multiple of 3998 and 4004 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3998 and 4004, than apply into the LCM equation.

GCF(3998,4004) = 2
LCM(3998,4004) = ( 3998 × 4004) / 2
LCM(3998,4004) = 16007992 / 2
LCM(3998,4004) = 8003996

Properties of LCM 3998 and 4004

(i) The LCM of 4004 and 3998 is associative

LCM of 3998 and 4004 = LCM of 4004 and 3998

Related Least Common Multiples of 3998

Related Least Common Multiples of 4004

Frequently Asked Questions on LCM of 3998 and 4004

1. What is the LCM of 3998 and 4004?

Answer: LCM of 3998 and 4004 is 8003996.

2. What are the Factors of 3998?

Answer: Factors of 3998 are 1, 2, 1999, 3998. There are 4 integers that are factors of 3998. The greatest factor of 3998 is 3998.

3. What are the Factors of 4004?

Answer: Factors of 4004 are 1, 2, 4, 7, 11, 13, 14, 22, 26, 28, 44, 52, 77, 91, 143, 154, 182, 286, 308, 364, 572, 1001, 2002, 4004. There are 24 integers that are factors of 4004. The greatest factor of 4004 is 4004.

4. How to Find the LCM of 3998 and 4004?

Answer:

Least Common Multiple of 3998 and 4004 = 8003996

Step 1: Find the prime factorization of 3998

3998 = 2 x 1999

Step 2: Find the prime factorization of 4004

4004 = 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 = 8003996 = 2 x 2 x 7 x 11 x 13 x 1999

Step 4: Therefore, the least common multiple of 3998 and 4004 is 8003996.