Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 2067 and 2075 the smallest integer that is 4289025 that is divisible by both numbers.
Least Common Multiple (LCM) of 2067 and 2075 is 4289025.
LCM(2067,2075) = 4289025
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 2067 and 2075. First we will calculate the prime factors of 2067 and 2075.
Prime Factorization of 2067
3 | 2067 |
13 | 689 |
53 | 53 |
1 |
Prime factors of 2067 are 3, 13,53. Prime factorization of 2067 in exponential form is:
2067 = 31×131×531
Prime Factorization of 2075
5 | 2075 |
5 | 415 |
83 | 83 |
1 |
Prime factors of 2075 are 5,83. Prime factorization of 2075 in exponential form is:
2075 = 52×831
Now multiplying the highest exponent prime factors to calculate the LCM of 2067 and 2075.
LCM(2067,2075) = 31×52×131×531×831
LCM(2067,2075) = 4289025
Factors of 2067
List of positive integer factors of 2067 that divides 2067 without a remainder.
1, 3, 13, 39, 53, 159, 689, 2067
Factors of 2075
List of positive integer factors of 2075 that divides 2075 without a remainder.
1, 5, 25, 83, 415, 2075
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2067 and 2075, than apply into the LCM equation.
GCF(2067,2075) = 1
LCM(2067,2075) = ( 2067 × 2075) / 1
LCM(2067,2075) = 4289025 / 1
LCM(2067,2075) = 4289025
(i) The LCM of 2075 and 2067 is associative
LCM of 2067 and 2075 = LCM of 2075 and 2067
1. What is the LCM of 2067 and 2075?
Answer: LCM of 2067 and 2075 is 4289025.
2. What are the Factors of 2067?
Answer: Factors of 2067 are 1, 3, 13, 39, 53, 159, 689, 2067. There are 8 integers that are factors of 2067. The greatest factor of 2067 is 2067.
3. What are the Factors of 2075?
Answer: Factors of 2075 are 1, 5, 25, 83, 415, 2075. There are 6 integers that are factors of 2075. The greatest factor of 2075 is 2075.
4. How to Find the LCM of 2067 and 2075?
Answer:
Least Common Multiple of 2067 and 2075 = 4289025
Step 1: Find the prime factorization of 2067
2067 = 3 x 13 x 53
Step 2: Find the prime factorization of 2075
2075 = 5 x 5 x 83
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 4289025 = 3 x 5 x 5 x 13 x 53 x 83
Step 4: Therefore, the least common multiple of 2067 and 2075 is 4289025.