Least Common Multiple of 1998 and 2006

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 2006 the smallest integer that is 2003994 that is divisible by both numbers.

Least Common Multiple (LCM) of 1998 and 2006 is 2003994.

LCM(1998,2006) = 2003994

LCM of 1998 and 2006

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

LCM of:
and

Least Common Multiple of 1998 and 2006

LCM of 1998 and 2006 is 2003994

Least common multiple can be found by multiplying the highest exponent prime factors of 1998 and 2006. First we will calculate the prime factors of 1998 and 2006.

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 2006


2 2006
17 1003
59 59
1

Prime factors of 2006 are 2, 17,59. Prime factorization of 2006 in exponential form is:

2006 = 21×171×591

Now multiplying the highest exponent prime factors to calculate the LCM of 1998 and 2006.

LCM(1998,2006) = 21×33×171×371×591
LCM(1998,2006) = 2003994

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 2006

List of positive integer factors of 2006 that divides 2006 without a remainder.

1, 2, 17, 34, 59, 118, 1003, 2006

Least Common Multiple of 1998 and 2006 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 2006, than apply into the LCM equation.

GCF(1998,2006) = 2
LCM(1998,2006) = ( 1998 × 2006) / 2
LCM(1998,2006) = 4007988 / 2
LCM(1998,2006) = 2003994

Properties of LCM 1998 and 2006

(i) The LCM of 2006 and 1998 is associative

LCM of 1998 and 2006 = LCM of 2006 and 1998

Related Least Common Multiples of 1998

Related Least Common Multiples of 2006

Frequently Asked Questions on LCM of 1998 and 2006

1. What is the LCM of 1998 and 2006?

Answer: LCM of 1998 and 2006 is 2003994.

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 2006?

Answer: Factors of 2006 are 1, 2, 17, 34, 59, 118, 1003, 2006. There are 8 integers that are factors of 2006. The greatest factor of 2006 is 2006.

4. How to Find the LCM of 1998 and 2006?

Answer:

Least Common Multiple of 1998 and 2006 = 2003994

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 2006

2006 = 2 x 17 x 59

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

LCM = 2003994 = 2 x 3 x 3 x 3 x 17 x 37 x 59

Step 4: Therefore, the least common multiple of 1998 and 2006 is 2003994.