Least Common Multiple of 1998 and 2004

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1998 and 2004 the smallest integer that is 667332 that is divisible by both numbers.

Least Common Multiple (LCM) of 1998 and 2004 is 667332.

LCM(1998,2004) = 667332

LCM of 1998 and 2004

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

LCM of:
and

Least Common Multiple of 1998 and 2004

LCM of 1998 and 2004 is 667332

Least common multiple can be found by multiplying the highest exponent prime factors of 1998 and 2004. First we will calculate the prime factors of 1998 and 2004.

Prime Factorization of 1998


2 1998
3 999
3 333
3 111
37 37
1

Prime factors of 1998 are 2, 3,37. Prime factorization of 1998 in exponential form is:

1998 = 21×33×371

Prime Factorization of 2004


2 2004
2 1002
3 501
167 167
1

Prime factors of 2004 are 2, 3,167. Prime factorization of 2004 in exponential form is:

2004 = 22×31×1671

Now multiplying the highest exponent prime factors to calculate the LCM of 1998 and 2004.

LCM(1998,2004) = 22×33×371×1671
LCM(1998,2004) = 667332

Factors of 1998

List of positive integer factors of 1998 that divides 1998 without a remainder.

1, 2, 3, 6, 9, 18, 27, 37, 54, 74, 111, 222, 333, 666, 999, 1998

Factors of 2004

List of positive integer factors of 2004 that divides 2004 without a remainder.

1, 2, 3, 4, 6, 12, 167, 334, 501, 668, 1002, 2004

Least Common Multiple of 1998 and 2004 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1998 and 2004, than apply into the LCM equation.

GCF(1998,2004) = 6
LCM(1998,2004) = ( 1998 × 2004) / 6
LCM(1998,2004) = 4003992 / 6
LCM(1998,2004) = 667332

Properties of LCM 1998 and 2004

(i) The LCM of 2004 and 1998 is associative

LCM of 1998 and 2004 = LCM of 2004 and 1998

Related Least Common Multiples of 1998

Related Least Common Multiples of 2004

Frequently Asked Questions on LCM of 1998 and 2004

1. What is the LCM of 1998 and 2004?

Answer: LCM of 1998 and 2004 is 667332.

2. What are the Factors of 1998?

Answer: Factors of 1998 are 1, 2, 3, 6, 9, 18, 27, 37, 54, 74, 111, 222, 333, 666, 999, 1998. There are 16 integers that are factors of 1998. The greatest factor of 1998 is 1998.

3. What are the Factors of 2004?

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

4. How to Find the LCM of 1998 and 2004?

Answer:

Least Common Multiple of 1998 and 2004 = 667332

Step 1: Find the prime factorization of 1998

1998 = 2 x 3 x 3 x 3 x 37

Step 2: Find the prime factorization of 2004

2004 = 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 = 667332 = 2 x 2 x 3 x 3 x 3 x 37 x 167

Step 4: Therefore, the least common multiple of 1998 and 2004 is 667332.