Least Common Multiple of 1989 and 1997

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1989 and 1997 the smallest integer that is 3972033 that is divisible by both numbers.

Least Common Multiple (LCM) of 1989 and 1997 is 3972033.

LCM(1989,1997) = 3972033

LCM of 1989 and 1997

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

LCM of:
and

Least Common Multiple of 1989 and 1997

LCM of 1989 and 1997 is 3972033

Least common multiple can be found by multiplying the highest exponent prime factors of 1989 and 1997. First we will calculate the prime factors of 1989 and 1997.

Prime Factorization of 1989


3 1989
3 663
13 221
17 17
1

Prime factors of 1989 are 3, 13,17. Prime factorization of 1989 in exponential form is:

1989 = 32×131×171

Prime Factorization of 1997


1997 1997
1

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

1997 = 19971

Now multiplying the highest exponent prime factors to calculate the LCM of 1989 and 1997.

LCM(1989,1997) = 32×131×171×19971
LCM(1989,1997) = 3972033

Factors of 1989

List of positive integer factors of 1989 that divides 1989 without a remainder.

1, 3, 9, 13, 17, 39, 51, 117, 153, 221, 663, 1989

Factors of 1997

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

1, 1997

Least Common Multiple of 1989 and 1997 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1989 and 1997, than apply into the LCM equation.

GCF(1989,1997) = 1
LCM(1989,1997) = ( 1989 × 1997) / 1
LCM(1989,1997) = 3972033 / 1
LCM(1989,1997) = 3972033

Properties of LCM 1989 and 1997

(i) The LCM of 1997 and 1989 is associative

LCM of 1989 and 1997 = LCM of 1997 and 1989

Related Least Common Multiples of 1989

Related Least Common Multiples of 1997

Frequently Asked Questions on LCM of 1989 and 1997

1. What is the LCM of 1989 and 1997?

Answer: LCM of 1989 and 1997 is 3972033.

2. What are the Factors of 1989?

Answer: Factors of 1989 are 1, 3, 9, 13, 17, 39, 51, 117, 153, 221, 663, 1989. There are 12 integers that are factors of 1989. The greatest factor of 1989 is 1989.

3. 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.

4. How to Find the LCM of 1989 and 1997?

Answer:

Least Common Multiple of 1989 and 1997 = 3972033

Step 1: Find the prime factorization of 1989

1989 = 3 x 3 x 13 x 17

Step 2: Find the prime factorization of 1997

1997 = 1997

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

LCM = 3972033 = 3 x 3 x 13 x 17 x 1997

Step 4: Therefore, the least common multiple of 1989 and 1997 is 3972033.