Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1030 and 1034 the smallest integer that is 532510 that is divisible by both numbers.
Least Common Multiple (LCM) of 1030 and 1034 is 532510.
LCM(1030,1034) = 532510
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 1030 and 1034. First we will calculate the prime factors of 1030 and 1034.
Prime Factorization of 1030
2 | 1030 |
5 | 515 |
103 | 103 |
1 |
Prime factors of 1030 are 2, 5,103. Prime factorization of 1030 in exponential form is:
1030 = 21×51×1031
Prime Factorization of 1034
2 | 1034 |
11 | 517 |
47 | 47 |
1 |
Prime factors of 1034 are 2, 11,47. Prime factorization of 1034 in exponential form is:
1034 = 21×111×471
Now multiplying the highest exponent prime factors to calculate the LCM of 1030 and 1034.
LCM(1030,1034) = 21×51×111×471×1031
LCM(1030,1034) = 532510
Factors of 1030
List of positive integer factors of 1030 that divides 1030 without a remainder.
1, 2, 5, 10, 103, 206, 515, 1030
Factors of 1034
List of positive integer factors of 1034 that divides 1034 without a remainder.
1, 2, 11, 22, 47, 94, 517, 1034
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1030 and 1034, than apply into the LCM equation.
GCF(1030,1034) = 2
LCM(1030,1034) = ( 1030 × 1034) / 2
LCM(1030,1034) = 1065020 / 2
LCM(1030,1034) = 532510
(i) The LCM of 1034 and 1030 is associative
LCM of 1030 and 1034 = LCM of 1034 and 1030
1. What is the LCM of 1030 and 1034?
Answer: LCM of 1030 and 1034 is 532510.
2. What are the Factors of 1030?
Answer: Factors of 1030 are 1, 2, 5, 10, 103, 206, 515, 1030. There are 8 integers that are factors of 1030. The greatest factor of 1030 is 1030.
3. What are the Factors of 1034?
Answer: Factors of 1034 are 1, 2, 11, 22, 47, 94, 517, 1034. There are 8 integers that are factors of 1034. The greatest factor of 1034 is 1034.
4. How to Find the LCM of 1030 and 1034?
Answer:
Least Common Multiple of 1030 and 1034 = 532510
Step 1: Find the prime factorization of 1030
1030 = 2 x 5 x 103
Step 2: Find the prime factorization of 1034
1034 = 2 x 11 x 47
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 532510 = 2 x 5 x 11 x 47 x 103
Step 4: Therefore, the least common multiple of 1030 and 1034 is 532510.