Least Common Multiple of 2024 and 2028
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 2024 and 2028 the smallest integer that is 1026168 that is divisible by both numbers.
Least Common Multiple (LCM) of 2024 and 2028 is 1026168.
LCM(2024,2028) = 1026168
LCM of 2024 and 2028
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 2024 and 2028 by Prime method
- Least Common Multiple of 2024 and 2028 with GCF Formula
LCM of 2024 and 2028 is 1026168
Least common multiple can be found by multiplying the highest exponent prime factors of 2024 and 2028. First we will calculate the prime factors of 2024 and 2028.
Prime Factorization of 2024
| 2 | 2024 |
| 2 | 1012 |
| 2 | 506 |
| 11 | 253 |
| 23 | 23 |
| 1 |
Prime factors of 2024 are 2, 11,23. Prime factorization of 2024 in exponential form is:
2024 = 23×111×231
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
Now multiplying the highest exponent prime factors to calculate the LCM of 2024 and 2028.
LCM(2024,2028) = 23×31×111×132×231
LCM(2024,2028) = 1026168
Factors of 2024
List of positive integer factors of 2024 that divides 2024 without a remainder.
1, 2, 4, 8, 11, 22, 23, 44, 46, 88, 92, 184, 253, 506, 1012, 2024
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
Least Common Multiple of 2024 and 2028 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2024 and 2028, than apply into the LCM equation.
GCF(2024,2028) = 4
LCM(2024,2028) = ( 2024 × 2028) / 4
LCM(2024,2028) = 4104672 / 4
LCM(2024,2028) = 1026168
Properties of LCM 2024 and 2028
(i) The LCM of 2028 and 2024 is associative
LCM of 2024 and 2028 = LCM of 2028 and 2024
Related Least Common Multiples of 2024
Related Least Common Multiples of 2028
Frequently Asked Questions on LCM of 2024 and 2028
1. What is the LCM of 2024 and 2028?
Answer: LCM of 2024 and 2028 is 1026168.
2. What are the Factors of 2024?
Answer: Factors of 2024 are 1, 2, 4, 8, 11, 22, 23, 44, 46, 88, 92, 184, 253, 506, 1012, 2024. There are 16 integers that are factors of 2024. The greatest factor of 2024 is 2024.
3. 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.
4. How to Find the LCM of 2024 and 2028?
Answer:
Least Common Multiple of 2024 and 2028 = 1026168
Step 1: Find the prime factorization of 2024
2024 = 2 x 2 x 2 x 11 x 23
Step 2: Find the prime factorization of 2028
2028 = 2 x 2 x 3 x 13 x 13
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 1026168 = 2 x 2 x 2 x 3 x 11 x 13 x 13 x 23
Step 4: Therefore, the least common multiple of 2024 and 2028 is 1026168.