Least Common Multiple of 1998 and 2002

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 2002 the smallest integer that is 1999998 that is divisible by both numbers.

Least Common Multiple (LCM) of 1998 and 2002 is 1999998.

LCM(1998,2002) = 1999998

LCM of 1998 and 2002

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

LCM of:
and

Least Common Multiple of 1998 and 2002

LCM of 1998 and 2002 is 1999998

Least common multiple can be found by multiplying the highest exponent prime factors of 1998 and 2002. First we will calculate the prime factors of 1998 and 2002.

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 2002


2 2002
7 1001
11 143
13 13
1

Prime factors of 2002 are 2, 7, 11,13. Prime factorization of 2002 in exponential form is:

2002 = 21×71×111×131

Now multiplying the highest exponent prime factors to calculate the LCM of 1998 and 2002.

LCM(1998,2002) = 21×33×71×111×131×371
LCM(1998,2002) = 1999998

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 2002

List of positive integer factors of 2002 that divides 2002 without a remainder.

1, 2, 7, 11, 13, 14, 22, 26, 77, 91, 143, 154, 182, 286, 1001, 2002

Least Common Multiple of 1998 and 2002 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 2002, than apply into the LCM equation.

GCF(1998,2002) = 2
LCM(1998,2002) = ( 1998 × 2002) / 2
LCM(1998,2002) = 3999996 / 2
LCM(1998,2002) = 1999998

Properties of LCM 1998 and 2002

(i) The LCM of 2002 and 1998 is associative

LCM of 1998 and 2002 = LCM of 2002 and 1998

Related Least Common Multiples of 1998

Related Least Common Multiples of 2002

Frequently Asked Questions on LCM of 1998 and 2002

1. What is the LCM of 1998 and 2002?

Answer: LCM of 1998 and 2002 is 1999998.

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 2002?

Answer: Factors of 2002 are 1, 2, 7, 11, 13, 14, 22, 26, 77, 91, 143, 154, 182, 286, 1001, 2002. There are 16 integers that are factors of 2002. The greatest factor of 2002 is 2002.

4. How to Find the LCM of 1998 and 2002?

Answer:

Least Common Multiple of 1998 and 2002 = 1999998

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 2002

2002 = 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 = 1999998 = 2 x 3 x 3 x 3 x 7 x 11 x 13 x 37

Step 4: Therefore, the least common multiple of 1998 and 2002 is 1999998.