Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1993 and 1996 the smallest integer that is 3978028 that is divisible by both numbers.
Least Common Multiple (LCM) of 1993 and 1996 is 3978028.
LCM(1993,1996) = 3978028
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 1993 and 1996. First we will calculate the prime factors of 1993 and 1996.
Prime Factorization of 1993
1993 | 1993 |
1 |
Prime factors of 1993 are 1993. Prime factorization of 1993 in exponential form is:
1993 = 19931
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 1993 and 1996.
LCM(1993,1996) = 22×4991×19931
LCM(1993,1996) = 3978028
Factors of 1993
List of positive integer factors of 1993 that divides 1993 without a remainder.
1, 1993
Factors of 1996
List of positive integer factors of 1996 that divides 1996 without a remainder.
1, 2, 4, 499, 998, 1996
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1993 and 1996, than apply into the LCM equation.
GCF(1993,1996) = 1
LCM(1993,1996) = ( 1993 × 1996) / 1
LCM(1993,1996) = 3978028 / 1
LCM(1993,1996) = 3978028
(i) The LCM of 1996 and 1993 is associative
LCM of 1993 and 1996 = LCM of 1996 and 1993
1. What is the LCM of 1993 and 1996?
Answer: LCM of 1993 and 1996 is 3978028.
2. What are the Factors of 1993?
Answer: Factors of 1993 are 1, 1993. There are 2 integers that are factors of 1993. The greatest factor of 1993 is 1993.
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 1993 and 1996?
Answer:
Least Common Multiple of 1993 and 1996 = 3978028
Step 1: Find the prime factorization of 1993
1993 = 1993
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 = 3978028 = 2 x 2 x 499 x 1993
Step 4: Therefore, the least common multiple of 1993 and 1996 is 3978028.