Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1995 and 1997 the smallest integer that is 3984015 that is divisible by both numbers.
Least Common Multiple (LCM) of 1995 and 1997 is 3984015.
LCM(1995,1997) = 3984015
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
Least common multiple can be found by multiplying the highest exponent prime factors of 1995 and 1997. First we will calculate the prime factors of 1995 and 1997.
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
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 1995 and 1997.
LCM(1995,1997) = 31×51×71×191×19971
LCM(1995,1997) = 3984015
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
Factors of 1997
List of positive integer factors of 1997 that divides 1997 without a remainder.
1, 1997
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1995 and 1997, than apply into the LCM equation.
GCF(1995,1997) = 1
LCM(1995,1997) = ( 1995 × 1997) / 1
LCM(1995,1997) = 3984015 / 1
LCM(1995,1997) = 3984015
(i) The LCM of 1997 and 1995 is associative
LCM of 1995 and 1997 = LCM of 1997 and 1995
1. What is the LCM of 1995 and 1997?
Answer: LCM of 1995 and 1997 is 3984015.
2. 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.
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 1995 and 1997?
Answer:
Least Common Multiple of 1995 and 1997 = 3984015
Step 1: Find the prime factorization of 1995
1995 = 3 x 5 x 7 x 19
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 = 3984015 = 3 x 5 x 7 x 19 x 1997
Step 4: Therefore, the least common multiple of 1995 and 1997 is 3984015.