Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 2030 and 2033 the smallest integer that is 4126990 that is divisible by both numbers.
Least Common Multiple (LCM) of 2030 and 2033 is 4126990.
LCM(2030,2033) = 4126990
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 2030 and 2033. First we will calculate the prime factors of 2030 and 2033.
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
Prime Factorization of 2033
19 | 2033 |
107 | 107 |
1 |
Prime factors of 2033 are 19,107. Prime factorization of 2033 in exponential form is:
2033 = 191×1071
Now multiplying the highest exponent prime factors to calculate the LCM of 2030 and 2033.
LCM(2030,2033) = 21×51×71×191×291×1071
LCM(2030,2033) = 4126990
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
Factors of 2033
List of positive integer factors of 2033 that divides 2033 without a remainder.
1, 19, 107, 2033
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2030 and 2033, than apply into the LCM equation.
GCF(2030,2033) = 1
LCM(2030,2033) = ( 2030 × 2033) / 1
LCM(2030,2033) = 4126990 / 1
LCM(2030,2033) = 4126990
(i) The LCM of 2033 and 2030 is associative
LCM of 2030 and 2033 = LCM of 2033 and 2030
1. What is the LCM of 2030 and 2033?
Answer: LCM of 2030 and 2033 is 4126990.
2. 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.
3. What are the Factors of 2033?
Answer: Factors of 2033 are 1, 19, 107, 2033. There are 4 integers that are factors of 2033. The greatest factor of 2033 is 2033.
4. How to Find the LCM of 2030 and 2033?
Answer:
Least Common Multiple of 2030 and 2033 = 4126990
Step 1: Find the prime factorization of 2030
2030 = 2 x 5 x 7 x 29
Step 2: Find the prime factorization of 2033
2033 = 19 x 107
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 4126990 = 2 x 5 x 7 x 19 x 29 x 107
Step 4: Therefore, the least common multiple of 2030 and 2033 is 4126990.