Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 2029 and 2030 the smallest integer that is 4118870 that is divisible by both numbers.
Least Common Multiple (LCM) of 2029 and 2030 is 4118870.
LCM(2029,2030) = 4118870
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 2029 and 2030. First we will calculate the prime factors of 2029 and 2030.
Prime Factorization of 2029
2029 | 2029 |
1 |
Prime factors of 2029 are 2029. Prime factorization of 2029 in exponential form is:
2029 = 20291
Prime Factorization of 2030
2 | 2030 |
5 | 1015 |
7 | 203 |
29 | 29 |
1 |
Prime factors of 2030 are 2, 5, 7,29. Prime factorization of 2030 in exponential form is:
2030 = 21×51×71×291
Now multiplying the highest exponent prime factors to calculate the LCM of 2029 and 2030.
LCM(2029,2030) = 21×51×71×291×20291
LCM(2029,2030) = 4118870
Factors of 2029
List of positive integer factors of 2029 that divides 2029 without a remainder.
1, 2029
Factors of 2030
List of positive integer factors of 2030 that divides 2030 without a remainder.
1, 2, 5, 7, 10, 14, 29, 35, 58, 70, 145, 203, 290, 406, 1015, 2030
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2029 and 2030, than apply into the LCM equation.
GCF(2029,2030) = 1
LCM(2029,2030) = ( 2029 × 2030) / 1
LCM(2029,2030) = 4118870 / 1
LCM(2029,2030) = 4118870
(i) The LCM of 2030 and 2029 is associative
LCM of 2029 and 2030 = LCM of 2030 and 2029
1. What is the LCM of 2029 and 2030?
Answer: LCM of 2029 and 2030 is 4118870.
2. What are the Factors of 2029?
Answer: Factors of 2029 are 1, 2029. There are 2 integers that are factors of 2029. The greatest factor of 2029 is 2029.
3. What are the Factors of 2030?
Answer: Factors of 2030 are 1, 2, 5, 7, 10, 14, 29, 35, 58, 70, 145, 203, 290, 406, 1015, 2030. There are 16 integers that are factors of 2030. The greatest factor of 2030 is 2030.
4. How to Find the LCM of 2029 and 2030?
Answer:
Least Common Multiple of 2029 and 2030 = 4118870
Step 1: Find the prime factorization of 2029
2029 = 2029
Step 2: Find the prime factorization of 2030
2030 = 2 x 5 x 7 x 29
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 4118870 = 2 x 5 x 7 x 29 x 2029
Step 4: Therefore, the least common multiple of 2029 and 2030 is 4118870.