Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 2037 and 2038 the smallest integer that is 4151406 that is divisible by both numbers.
Least Common Multiple (LCM) of 2037 and 2038 is 4151406.
LCM(2037,2038) = 4151406
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 2037 and 2038. First we will calculate the prime factors of 2037 and 2038.
Prime Factorization of 2037
3 | 2037 |
7 | 679 |
97 | 97 |
1 |
Prime factors of 2037 are 3, 7,97. Prime factorization of 2037 in exponential form is:
2037 = 31×71×971
Prime Factorization of 2038
2 | 2038 |
1019 | 1019 |
1 |
Prime factors of 2038 are 2,1019. Prime factorization of 2038 in exponential form is:
2038 = 21×10191
Now multiplying the highest exponent prime factors to calculate the LCM of 2037 and 2038.
LCM(2037,2038) = 21×31×71×971×10191
LCM(2037,2038) = 4151406
Factors of 2037
List of positive integer factors of 2037 that divides 2037 without a remainder.
1, 3, 7, 21, 97, 291, 679, 2037
Factors of 2038
List of positive integer factors of 2038 that divides 2038 without a remainder.
1, 2, 1019, 2038
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2037 and 2038, than apply into the LCM equation.
GCF(2037,2038) = 1
LCM(2037,2038) = ( 2037 × 2038) / 1
LCM(2037,2038) = 4151406 / 1
LCM(2037,2038) = 4151406
(i) The LCM of 2038 and 2037 is associative
LCM of 2037 and 2038 = LCM of 2038 and 2037
1. What is the LCM of 2037 and 2038?
Answer: LCM of 2037 and 2038 is 4151406.
2. What are the Factors of 2037?
Answer: Factors of 2037 are 1, 3, 7, 21, 97, 291, 679, 2037. There are 8 integers that are factors of 2037. The greatest factor of 2037 is 2037.
3. What are the Factors of 2038?
Answer: Factors of 2038 are 1, 2, 1019, 2038. There are 4 integers that are factors of 2038. The greatest factor of 2038 is 2038.
4. How to Find the LCM of 2037 and 2038?
Answer:
Least Common Multiple of 2037 and 2038 = 4151406
Step 1: Find the prime factorization of 2037
2037 = 3 x 7 x 97
Step 2: Find the prime factorization of 2038
2038 = 2 x 1019
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 4151406 = 2 x 3 x 7 x 97 x 1019
Step 4: Therefore, the least common multiple of 2037 and 2038 is 4151406.