Least Common Multiple of 1989 and 1995

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 1995 the smallest integer that is 1322685 that is divisible by both numbers.

Least Common Multiple (LCM) of 1989 and 1995 is 1322685.

LCM(1989,1995) = 1322685

LCM of 1989 and 1995

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

LCM of:
and

Least Common Multiple of 1989 and 1995

LCM of 1989 and 1995 is 1322685

Least common multiple can be found by multiplying the highest exponent prime factors of 1989 and 1995. First we will calculate the prime factors of 1989 and 1995.

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 1995


3 1995
5 665
7 133
19 19
1

Prime factors of 1995 are 3, 5, 7,19. Prime factorization of 1995 in exponential form is:

1995 = 31×51×71×191

Now multiplying the highest exponent prime factors to calculate the LCM of 1989 and 1995.

LCM(1989,1995) = 32×51×71×131×171×191
LCM(1989,1995) = 1322685

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 1995

List of positive integer factors of 1995 that divides 1995 without a remainder.

1, 3, 5, 7, 15, 19, 21, 35, 57, 95, 105, 133, 285, 399, 665, 1995

Least Common Multiple of 1989 and 1995 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 1995, than apply into the LCM equation.

GCF(1989,1995) = 3
LCM(1989,1995) = ( 1989 × 1995) / 3
LCM(1989,1995) = 3968055 / 3
LCM(1989,1995) = 1322685

Properties of LCM 1989 and 1995

(i) The LCM of 1995 and 1989 is associative

LCM of 1989 and 1995 = LCM of 1995 and 1989

Related Least Common Multiples of 1989

Related Least Common Multiples of 1995

Frequently Asked Questions on LCM of 1989 and 1995

1. What is the LCM of 1989 and 1995?

Answer: LCM of 1989 and 1995 is 1322685.

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 1995?

Answer: Factors of 1995 are 1, 3, 5, 7, 15, 19, 21, 35, 57, 95, 105, 133, 285, 399, 665, 1995. There are 16 integers that are factors of 1995. The greatest factor of 1995 is 1995.

4. How to Find the LCM of 1989 and 1995?

Answer:

Least Common Multiple of 1989 and 1995 = 1322685

Step 1: Find the prime factorization of 1989

1989 = 3 x 3 x 13 x 17

Step 2: Find the prime factorization of 1995

1995 = 3 x 5 x 7 x 19

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

LCM = 1322685 = 3 x 3 x 5 x 7 x 13 x 17 x 19

Step 4: Therefore, the least common multiple of 1989 and 1995 is 1322685.