Least Common Multiple of 1997 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 1997 and 2004 the smallest integer that is 4001988 that is divisible by both numbers.

Least Common Multiple (LCM) of 1997 and 2004 is 4001988.

LCM(1997,2004) = 4001988

LCM of 1997 and 2004

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

LCM of:
and

Least Common Multiple of 1997 and 2004

LCM of 1997 and 2004 is 4001988

Least common multiple can be found by multiplying the highest exponent prime factors of 1997 and 2004. First we will calculate the prime factors of 1997 and 2004.

Prime Factorization of 1997


1997 1997
1

Prime factors of 1997 are 1997. Prime factorization of 1997 in exponential form is:

1997 = 19971

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 1997 and 2004.

LCM(1997,2004) = 22×31×1671×19971
LCM(1997,2004) = 4001988

Factors of 1997

List of positive integer factors of 1997 that divides 1997 without a remainder.

1, 1997

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 1997 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 1997 and 2004, than apply into the LCM equation.

GCF(1997,2004) = 1
LCM(1997,2004) = ( 1997 × 2004) / 1
LCM(1997,2004) = 4001988 / 1
LCM(1997,2004) = 4001988

Properties of LCM 1997 and 2004

(i) The LCM of 2004 and 1997 is associative

LCM of 1997 and 2004 = LCM of 2004 and 1997

Related Least Common Multiples of 1997

Related Least Common Multiples of 2004

Frequently Asked Questions on LCM of 1997 and 2004

1. What is the LCM of 1997 and 2004?

Answer: LCM of 1997 and 2004 is 4001988.

2. What are the Factors of 1997?

Answer: Factors of 1997 are 1, 1997. There are 2 integers that are factors of 1997. The greatest factor of 1997 is 1997.

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 1997 and 2004?

Answer:

Least Common Multiple of 1997 and 2004 = 4001988

Step 1: Find the prime factorization of 1997

1997 = 1997

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 = 4001988 = 2 x 2 x 3 x 167 x 1997

Step 4: Therefore, the least common multiple of 1997 and 2004 is 4001988.