Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1027 and 1028 the smallest integer that is 1055756 that is divisible by both numbers.
Least Common Multiple (LCM) of 1027 and 1028 is 1055756.
LCM(1027,1028) = 1055756
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 1027 and 1028. First we will calculate the prime factors of 1027 and 1028.
Prime Factorization of 1027
13 | 1027 |
79 | 79 |
1 |
Prime factors of 1027 are 13,79. Prime factorization of 1027 in exponential form is:
1027 = 131×791
Prime Factorization of 1028
2 | 1028 |
2 | 514 |
257 | 257 |
1 |
Prime factors of 1028 are 2,257. Prime factorization of 1028 in exponential form is:
1028 = 22×2571
Now multiplying the highest exponent prime factors to calculate the LCM of 1027 and 1028.
LCM(1027,1028) = 22×131×791×2571
LCM(1027,1028) = 1055756
Factors of 1027
List of positive integer factors of 1027 that divides 1027 without a remainder.
1, 13, 79, 1027
Factors of 1028
List of positive integer factors of 1028 that divides 1028 without a remainder.
1, 2, 4, 257, 514, 1028
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1027 and 1028, than apply into the LCM equation.
GCF(1027,1028) = 1
LCM(1027,1028) = ( 1027 × 1028) / 1
LCM(1027,1028) = 1055756 / 1
LCM(1027,1028) = 1055756
(i) The LCM of 1028 and 1027 is associative
LCM of 1027 and 1028 = LCM of 1028 and 1027
1. What is the LCM of 1027 and 1028?
Answer: LCM of 1027 and 1028 is 1055756.
2. What are the Factors of 1027?
Answer: Factors of 1027 are 1, 13, 79, 1027. There are 4 integers that are factors of 1027. The greatest factor of 1027 is 1027.
3. What are the Factors of 1028?
Answer: Factors of 1028 are 1, 2, 4, 257, 514, 1028. There are 6 integers that are factors of 1028. The greatest factor of 1028 is 1028.
4. How to Find the LCM of 1027 and 1028?
Answer:
Least Common Multiple of 1027 and 1028 = 1055756
Step 1: Find the prime factorization of 1027
1027 = 13 x 79
Step 2: Find the prime factorization of 1028
1028 = 2 x 2 x 257
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 1055756 = 2 x 2 x 13 x 79 x 257
Step 4: Therefore, the least common multiple of 1027 and 1028 is 1055756.