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 2036 the smallest integer that is 1032252 that is divisible by both numbers.
Least Common Multiple (LCM) of 2028 and 2036 is 1032252.
LCM(2028,2036) = 1032252
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 2036. First we will calculate the prime factors of 2028 and 2036.
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 2036
2 | 2036 |
2 | 1018 |
509 | 509 |
1 |
Prime factors of 2036 are 2,509. Prime factorization of 2036 in exponential form is:
2036 = 22×5091
Now multiplying the highest exponent prime factors to calculate the LCM of 2028 and 2036.
LCM(2028,2036) = 22×31×132×5091
LCM(2028,2036) = 1032252
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 2036
List of positive integer factors of 2036 that divides 2036 without a remainder.
1, 2, 4, 509, 1018, 2036
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2028 and 2036, than apply into the LCM equation.
GCF(2028,2036) = 4
LCM(2028,2036) = ( 2028 × 2036) / 4
LCM(2028,2036) = 4129008 / 4
LCM(2028,2036) = 1032252
(i) The LCM of 2036 and 2028 is associative
LCM of 2028 and 2036 = LCM of 2036 and 2028
1. What is the LCM of 2028 and 2036?
Answer: LCM of 2028 and 2036 is 1032252.
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 2036?
Answer: Factors of 2036 are 1, 2, 4, 509, 1018, 2036. There are 6 integers that are factors of 2036. The greatest factor of 2036 is 2036.
4. How to Find the LCM of 2028 and 2036?
Answer:
Least Common Multiple of 2028 and 2036 = 1032252
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 2036
2036 = 2 x 2 x 509
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 1032252 = 2 x 2 x 3 x 13 x 13 x 509
Step 4: Therefore, the least common multiple of 2028 and 2036 is 1032252.