Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 2667 and 2675 the smallest integer that is 7134225 that is divisible by both numbers.
Least Common Multiple (LCM) of 2667 and 2675 is 7134225.
LCM(2667,2675) = 7134225
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 2667 and 2675. First we will calculate the prime factors of 2667 and 2675.
Prime Factorization of 2667
3 | 2667 |
7 | 889 |
127 | 127 |
1 |
Prime factors of 2667 are 3, 7,127. Prime factorization of 2667 in exponential form is:
2667 = 31×71×1271
Prime Factorization of 2675
5 | 2675 |
5 | 535 |
107 | 107 |
1 |
Prime factors of 2675 are 5,107. Prime factorization of 2675 in exponential form is:
2675 = 52×1071
Now multiplying the highest exponent prime factors to calculate the LCM of 2667 and 2675.
LCM(2667,2675) = 31×52×71×1071×1271
LCM(2667,2675) = 7134225
Factors of 2667
List of positive integer factors of 2667 that divides 2667 without a remainder.
1, 3, 7, 21, 127, 381, 889, 2667
Factors of 2675
List of positive integer factors of 2675 that divides 2675 without a remainder.
1, 5, 25, 107, 535, 2675
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2667 and 2675, than apply into the LCM equation.
GCF(2667,2675) = 1
LCM(2667,2675) = ( 2667 × 2675) / 1
LCM(2667,2675) = 7134225 / 1
LCM(2667,2675) = 7134225
(i) The LCM of 2675 and 2667 is associative
LCM of 2667 and 2675 = LCM of 2675 and 2667
1. What is the LCM of 2667 and 2675?
Answer: LCM of 2667 and 2675 is 7134225.
2. What are the Factors of 2667?
Answer: Factors of 2667 are 1, 3, 7, 21, 127, 381, 889, 2667. There are 8 integers that are factors of 2667. The greatest factor of 2667 is 2667.
3. What are the Factors of 2675?
Answer: Factors of 2675 are 1, 5, 25, 107, 535, 2675. There are 6 integers that are factors of 2675. The greatest factor of 2675 is 2675.
4. How to Find the LCM of 2667 and 2675?
Answer:
Least Common Multiple of 2667 and 2675 = 7134225
Step 1: Find the prime factorization of 2667
2667 = 3 x 7 x 127
Step 2: Find the prime factorization of 2675
2675 = 5 x 5 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 = 7134225 = 3 x 5 x 5 x 7 x 107 x 127
Step 4: Therefore, the least common multiple of 2667 and 2675 is 7134225.