Least Common Multiple of 1998 and 2000

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 2000 the smallest integer that is 1998000 that is divisible by both numbers.

Least Common Multiple (LCM) of 1998 and 2000 is 1998000.

LCM(1998,2000) = 1998000

LCM of 1998 and 2000

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

LCM of:
and

Least Common Multiple of 1998 and 2000

LCM of 1998 and 2000 is 1998000

Least common multiple can be found by multiplying the highest exponent prime factors of 1998 and 2000. First we will calculate the prime factors of 1998 and 2000.

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 2000


2 2000
2 1000
2 500
2 250
5 125
5 25
5 5
1

Prime factors of 2000 are 2,5. Prime factorization of 2000 in exponential form is:

2000 = 24×53

Now multiplying the highest exponent prime factors to calculate the LCM of 1998 and 2000.

LCM(1998,2000) = 24×33×53×371
LCM(1998,2000) = 1998000

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 2000

List of positive integer factors of 2000 that divides 2000 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 1000, 2000

Least Common Multiple of 1998 and 2000 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 2000, than apply into the LCM equation.

GCF(1998,2000) = 2
LCM(1998,2000) = ( 1998 × 2000) / 2
LCM(1998,2000) = 3996000 / 2
LCM(1998,2000) = 1998000

Properties of LCM 1998 and 2000

(i) The LCM of 2000 and 1998 is associative

LCM of 1998 and 2000 = LCM of 2000 and 1998

Related Least Common Multiples of 1998

Related Least Common Multiples of 2000

Frequently Asked Questions on LCM of 1998 and 2000

1. What is the LCM of 1998 and 2000?

Answer: LCM of 1998 and 2000 is 1998000.

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 2000?

Answer: Factors of 2000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 1000, 2000. There are 20 integers that are factors of 2000. The greatest factor of 2000 is 2000.

4. How to Find the LCM of 1998 and 2000?

Answer:

Least Common Multiple of 1998 and 2000 = 1998000

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 2000

2000 = 2 x 2 x 2 x 2 x 5 x 5 x 5

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

LCM = 1998000 = 2 x 2 x 2 x 2 x 3 x 3 x 3 x 5 x 5 x 5 x 37

Step 4: Therefore, the least common multiple of 1998 and 2000 is 1998000.