Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 2020 and 2022 the smallest integer that is 2042220 that is divisible by both numbers.
Least Common Multiple (LCM) of 2020 and 2022 is 2042220.
LCM(2020,2022) = 2042220
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 2020 and 2022. First we will calculate the prime factors of 2020 and 2022.
Prime Factorization of 2020
2 | 2020 |
2 | 1010 |
5 | 505 |
101 | 101 |
1 |
Prime factors of 2020 are 2, 5,101. Prime factorization of 2020 in exponential form is:
2020 = 22×51×1011
Prime Factorization of 2022
2 | 2022 |
3 | 1011 |
337 | 337 |
1 |
Prime factors of 2022 are 2, 3,337. Prime factorization of 2022 in exponential form is:
2022 = 21×31×3371
Now multiplying the highest exponent prime factors to calculate the LCM of 2020 and 2022.
LCM(2020,2022) = 22×31×51×1011×3371
LCM(2020,2022) = 2042220
Factors of 2020
List of positive integer factors of 2020 that divides 2020 without a remainder.
1, 2, 4, 5, 10, 20, 101, 202, 404, 505, 1010, 2020
Factors of 2022
List of positive integer factors of 2022 that divides 2022 without a remainder.
1, 2, 3, 6, 337, 674, 1011, 2022
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2020 and 2022, than apply into the LCM equation.
GCF(2020,2022) = 2
LCM(2020,2022) = ( 2020 × 2022) / 2
LCM(2020,2022) = 4084440 / 2
LCM(2020,2022) = 2042220
(i) The LCM of 2022 and 2020 is associative
LCM of 2020 and 2022 = LCM of 2022 and 2020
1. What is the LCM of 2020 and 2022?
Answer: LCM of 2020 and 2022 is 2042220.
2. What are the Factors of 2020?
Answer: Factors of 2020 are 1, 2, 4, 5, 10, 20, 101, 202, 404, 505, 1010, 2020. There are 12 integers that are factors of 2020. The greatest factor of 2020 is 2020.
3. What are the Factors of 2022?
Answer: Factors of 2022 are 1, 2, 3, 6, 337, 674, 1011, 2022. There are 8 integers that are factors of 2022. The greatest factor of 2022 is 2022.
4. How to Find the LCM of 2020 and 2022?
Answer:
Least Common Multiple of 2020 and 2022 = 2042220
Step 1: Find the prime factorization of 2020
2020 = 2 x 2 x 5 x 101
Step 2: Find the prime factorization of 2022
2022 = 2 x 3 x 337
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 2042220 = 2 x 2 x 3 x 5 x 101 x 337
Step 4: Therefore, the least common multiple of 2020 and 2022 is 2042220.