Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 2028 and 2030 the smallest integer that is 2058420 that is divisible by both numbers.
Least Common Multiple (LCM) of 2028 and 2030 is 2058420.
LCM(2028,2030) = 2058420
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 2028 and 2030. First we will calculate the prime factors of 2028 and 2030.
Prime Factorization of 2028
2 | 2028 |
2 | 1014 |
3 | 507 |
13 | 169 |
13 | 13 |
1 |
Prime factors of 2028 are 2, 3,13. Prime factorization of 2028 in exponential form is:
2028 = 22×31×132
Prime Factorization of 2030
2 | 2030 |
5 | 1015 |
7 | 203 |
29 | 29 |
1 |
Prime factors of 2030 are 2, 5, 7,29. Prime factorization of 2030 in exponential form is:
2030 = 21×51×71×291
Now multiplying the highest exponent prime factors to calculate the LCM of 2028 and 2030.
LCM(2028,2030) = 22×31×51×71×132×291
LCM(2028,2030) = 2058420
Factors of 2028
List of positive integer factors of 2028 that divides 2028 without a remainder.
1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156, 169, 338, 507, 676, 1014, 2028
Factors of 2030
List of positive integer factors of 2030 that divides 2030 without a remainder.
1, 2, 5, 7, 10, 14, 29, 35, 58, 70, 145, 203, 290, 406, 1015, 2030
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2028 and 2030, than apply into the LCM equation.
GCF(2028,2030) = 2
LCM(2028,2030) = ( 2028 × 2030) / 2
LCM(2028,2030) = 4116840 / 2
LCM(2028,2030) = 2058420
(i) The LCM of 2030 and 2028 is associative
LCM of 2028 and 2030 = LCM of 2030 and 2028
1. What is the LCM of 2028 and 2030?
Answer: LCM of 2028 and 2030 is 2058420.
2. What are the Factors of 2028?
Answer: Factors of 2028 are 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156, 169, 338, 507, 676, 1014, 2028. There are 18 integers that are factors of 2028. The greatest factor of 2028 is 2028.
3. What are the Factors of 2030?
Answer: Factors of 2030 are 1, 2, 5, 7, 10, 14, 29, 35, 58, 70, 145, 203, 290, 406, 1015, 2030. There are 16 integers that are factors of 2030. The greatest factor of 2030 is 2030.
4. How to Find the LCM of 2028 and 2030?
Answer:
Least Common Multiple of 2028 and 2030 = 2058420
Step 1: Find the prime factorization of 2028
2028 = 2 x 2 x 3 x 13 x 13
Step 2: Find the prime factorization of 2030
2030 = 2 x 5 x 7 x 29
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 2058420 = 2 x 2 x 3 x 5 x 7 x 13 x 13 x 29
Step 4: Therefore, the least common multiple of 2028 and 2030 is 2058420.