Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1028 and 1029 the smallest integer that is 1057812 that is divisible by both numbers.
Least Common Multiple (LCM) of 1028 and 1029 is 1057812.
LCM(1028,1029) = 1057812
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 1028 and 1029. First we will calculate the prime factors of 1028 and 1029.
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
Prime Factorization of 1029
3 | 1029 |
7 | 343 |
7 | 49 |
7 | 7 |
1 |
Prime factors of 1029 are 3,7. Prime factorization of 1029 in exponential form is:
1029 = 31×73
Now multiplying the highest exponent prime factors to calculate the LCM of 1028 and 1029.
LCM(1028,1029) = 22×31×73×2571
LCM(1028,1029) = 1057812
Factors of 1028
List of positive integer factors of 1028 that divides 1028 without a remainder.
1, 2, 4, 257, 514, 1028
Factors of 1029
List of positive integer factors of 1029 that divides 1029 without a remainder.
1, 3, 7, 21, 49, 147, 343, 1029
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1028 and 1029, than apply into the LCM equation.
GCF(1028,1029) = 1
LCM(1028,1029) = ( 1028 × 1029) / 1
LCM(1028,1029) = 1057812 / 1
LCM(1028,1029) = 1057812
(i) The LCM of 1029 and 1028 is associative
LCM of 1028 and 1029 = LCM of 1029 and 1028
1. What is the LCM of 1028 and 1029?
Answer: LCM of 1028 and 1029 is 1057812.
2. 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.
3. What are the Factors of 1029?
Answer: Factors of 1029 are 1, 3, 7, 21, 49, 147, 343, 1029. There are 8 integers that are factors of 1029. The greatest factor of 1029 is 1029.
4. How to Find the LCM of 1028 and 1029?
Answer:
Least Common Multiple of 1028 and 1029 = 1057812
Step 1: Find the prime factorization of 1028
1028 = 2 x 2 x 257
Step 2: Find the prime factorization of 1029
1029 = 3 x 7 x 7 x 7
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 1057812 = 2 x 2 x 3 x 7 x 7 x 7 x 257
Step 4: Therefore, the least common multiple of 1028 and 1029 is 1057812.