Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 6740 and 6746 the smallest integer that is 22734020 that is divisible by both numbers.
Least Common Multiple (LCM) of 6740 and 6746 is 22734020.
LCM(6740,6746) = 22734020
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 6740 and 6746. First we will calculate the prime factors of 6740 and 6746.
Prime Factorization of 6740
2 | 6740 |
2 | 3370 |
5 | 1685 |
337 | 337 |
1 |
Prime factors of 6740 are 2, 5,337. Prime factorization of 6740 in exponential form is:
6740 = 22×51×3371
Prime Factorization of 6746
2 | 6746 |
3373 | 3373 |
1 |
Prime factors of 6746 are 2,3373. Prime factorization of 6746 in exponential form is:
6746 = 21×33731
Now multiplying the highest exponent prime factors to calculate the LCM of 6740 and 6746.
LCM(6740,6746) = 22×51×3371×33731
LCM(6740,6746) = 22734020
Factors of 6740
List of positive integer factors of 6740 that divides 6740 without a remainder.
1, 2, 4, 5, 10, 20, 337, 674, 1348, 1685, 3370, 6740
Factors of 6746
List of positive integer factors of 6746 that divides 6746 without a remainder.
1, 2, 3373, 6746
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6740 and 6746, than apply into the LCM equation.
GCF(6740,6746) = 2
LCM(6740,6746) = ( 6740 × 6746) / 2
LCM(6740,6746) = 45468040 / 2
LCM(6740,6746) = 22734020
(i) The LCM of 6746 and 6740 is associative
LCM of 6740 and 6746 = LCM of 6746 and 6740
1. What is the LCM of 6740 and 6746?
Answer: LCM of 6740 and 6746 is 22734020.
2. What are the Factors of 6740?
Answer: Factors of 6740 are 1, 2, 4, 5, 10, 20, 337, 674, 1348, 1685, 3370, 6740. There are 12 integers that are factors of 6740. The greatest factor of 6740 is 6740.
3. What are the Factors of 6746?
Answer: Factors of 6746 are 1, 2, 3373, 6746. There are 4 integers that are factors of 6746. The greatest factor of 6746 is 6746.
4. How to Find the LCM of 6740 and 6746?
Answer:
Least Common Multiple of 6740 and 6746 = 22734020
Step 1: Find the prime factorization of 6740
6740 = 2 x 2 x 5 x 337
Step 2: Find the prime factorization of 6746
6746 = 2 x 3373
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 22734020 = 2 x 2 x 5 x 337 x 3373
Step 4: Therefore, the least common multiple of 6740 and 6746 is 22734020.