Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1029 and 1031 the smallest integer that is 1060899 that is divisible by both numbers.
Least Common Multiple (LCM) of 1029 and 1031 is 1060899.
LCM(1029,1031) = 1060899
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 1029 and 1031. First we will calculate the prime factors of 1029 and 1031.
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
Prime Factorization of 1031
1031 | 1031 |
1 |
Prime factors of 1031 are 1031. Prime factorization of 1031 in exponential form is:
1031 = 10311
Now multiplying the highest exponent prime factors to calculate the LCM of 1029 and 1031.
LCM(1029,1031) = 31×73×10311
LCM(1029,1031) = 1060899
Factors of 1029
List of positive integer factors of 1029 that divides 1029 without a remainder.
1, 3, 7, 21, 49, 147, 343, 1029
Factors of 1031
List of positive integer factors of 1031 that divides 1031 without a remainder.
1, 1031
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1029 and 1031, than apply into the LCM equation.
GCF(1029,1031) = 1
LCM(1029,1031) = ( 1029 × 1031) / 1
LCM(1029,1031) = 1060899 / 1
LCM(1029,1031) = 1060899
(i) The LCM of 1031 and 1029 is associative
LCM of 1029 and 1031 = LCM of 1031 and 1029
1. What is the LCM of 1029 and 1031?
Answer: LCM of 1029 and 1031 is 1060899.
2. 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.
3. What are the Factors of 1031?
Answer: Factors of 1031 are 1, 1031. There are 2 integers that are factors of 1031. The greatest factor of 1031 is 1031.
4. How to Find the LCM of 1029 and 1031?
Answer:
Least Common Multiple of 1029 and 1031 = 1060899
Step 1: Find the prime factorization of 1029
1029 = 3 x 7 x 7 x 7
Step 2: Find the prime factorization of 1031
1031 = 1031
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 1060899 = 3 x 7 x 7 x 7 x 1031
Step 4: Therefore, the least common multiple of 1029 and 1031 is 1060899.