Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 2040 and 2043 the smallest integer that is 1389240 that is divisible by both numbers.
Least Common Multiple (LCM) of 2040 and 2043 is 1389240.
LCM(2040,2043) = 1389240
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 2040 and 2043. First we will calculate the prime factors of 2040 and 2043.
Prime Factorization of 2040
2 | 2040 |
2 | 1020 |
2 | 510 |
3 | 255 |
5 | 85 |
17 | 17 |
1 |
Prime factors of 2040 are 2, 3, 5,17. Prime factorization of 2040 in exponential form is:
2040 = 23×31×51×171
Prime Factorization of 2043
3 | 2043 |
3 | 681 |
227 | 227 |
1 |
Prime factors of 2043 are 3,227. Prime factorization of 2043 in exponential form is:
2043 = 32×2271
Now multiplying the highest exponent prime factors to calculate the LCM of 2040 and 2043.
LCM(2040,2043) = 23×32×51×171×2271
LCM(2040,2043) = 1389240
Factors of 2040
List of positive integer factors of 2040 that divides 2040 without a remainder.
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 17, 20, 24, 30, 34, 40, 51, 60, 68, 85, 102, 120, 136, 170, 204, 255, 340, 408, 510, 680, 1020, 2040
Factors of 2043
List of positive integer factors of 2043 that divides 2043 without a remainder.
1, 3, 9, 227, 681, 2043
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2040 and 2043, than apply into the LCM equation.
GCF(2040,2043) = 3
LCM(2040,2043) = ( 2040 × 2043) / 3
LCM(2040,2043) = 4167720 / 3
LCM(2040,2043) = 1389240
(i) The LCM of 2043 and 2040 is associative
LCM of 2040 and 2043 = LCM of 2043 and 2040
1. What is the LCM of 2040 and 2043?
Answer: LCM of 2040 and 2043 is 1389240.
2. What are the Factors of 2040?
Answer: Factors of 2040 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 17, 20, 24, 30, 34, 40, 51, 60, 68, 85, 102, 120, 136, 170, 204, 255, 340, 408, 510, 680, 1020, 2040. There are 32 integers that are factors of 2040. The greatest factor of 2040 is 2040.
3. What are the Factors of 2043?
Answer: Factors of 2043 are 1, 3, 9, 227, 681, 2043. There are 6 integers that are factors of 2043. The greatest factor of 2043 is 2043.
4. How to Find the LCM of 2040 and 2043?
Answer:
Least Common Multiple of 2040 and 2043 = 1389240
Step 1: Find the prime factorization of 2040
2040 = 2 x 2 x 2 x 3 x 5 x 17
Step 2: Find the prime factorization of 2043
2043 = 3 x 3 x 227
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 1389240 = 2 x 2 x 2 x 3 x 3 x 5 x 17 x 227
Step 4: Therefore, the least common multiple of 2040 and 2043 is 1389240.