Least Common Multiple of 1989 and 1996
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 1996 the smallest integer that is 3970044 that is divisible by both numbers.
Least Common Multiple (LCM) of 1989 and 1996 is 3970044.
LCM(1989,1996) = 3970044
LCM of 1989 and 1996
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 1989 and 1996 by Prime method
- Least Common Multiple of 1989 and 1996 with GCF Formula
LCM of 1989 and 1996 is 3970044
Least common multiple can be found by multiplying the highest exponent prime factors of 1989 and 1996. First we will calculate the prime factors of 1989 and 1996.
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 1996
| 2 | 1996 |
| 2 | 998 |
| 499 | 499 |
| 1 |
Prime factors of 1996 are 2,499. Prime factorization of 1996 in exponential form is:
1996 = 22×4991
Now multiplying the highest exponent prime factors to calculate the LCM of 1989 and 1996.
LCM(1989,1996) = 22×32×131×171×4991
LCM(1989,1996) = 3970044
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 1996
List of positive integer factors of 1996 that divides 1996 without a remainder.
1, 2, 4, 499, 998, 1996
Least Common Multiple of 1989 and 1996 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 1996, than apply into the LCM equation.
GCF(1989,1996) = 1
LCM(1989,1996) = ( 1989 × 1996) / 1
LCM(1989,1996) = 3970044 / 1
LCM(1989,1996) = 3970044
Properties of LCM 1989 and 1996
(i) The LCM of 1996 and 1989 is associative
LCM of 1989 and 1996 = LCM of 1996 and 1989
Related Least Common Multiples of 1989
Related Least Common Multiples of 1996
Frequently Asked Questions on LCM of 1989 and 1996
1. What is the LCM of 1989 and 1996?
Answer: LCM of 1989 and 1996 is 3970044.
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 1996?
Answer: Factors of 1996 are 1, 2, 4, 499, 998, 1996. There are 6 integers that are factors of 1996. The greatest factor of 1996 is 1996.
4. How to Find the LCM of 1989 and 1996?
Answer:
Least Common Multiple of 1989 and 1996 = 3970044
Step 1: Find the prime factorization of 1989
1989 = 3 x 3 x 13 x 17
Step 2: Find the prime factorization of 1996
1996 = 2 x 2 x 499
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 3970044 = 2 x 2 x 3 x 3 x 13 x 17 x 499
Step 4: Therefore, the least common multiple of 1989 and 1996 is 3970044.