Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 6968 and 6975 the smallest integer that is 48601800 that is divisible by both numbers.
Least Common Multiple (LCM) of 6968 and 6975 is 48601800.
LCM(6968,6975) = 48601800
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 6968 and 6975. First we will calculate the prime factors of 6968 and 6975.
Prime Factorization of 6968
2 | 6968 |
2 | 3484 |
2 | 1742 |
13 | 871 |
67 | 67 |
1 |
Prime factors of 6968 are 2, 13,67. Prime factorization of 6968 in exponential form is:
6968 = 23×131×671
Prime Factorization of 6975
3 | 6975 |
3 | 2325 |
5 | 775 |
5 | 155 |
31 | 31 |
1 |
Prime factors of 6975 are 3, 5,31. Prime factorization of 6975 in exponential form is:
6975 = 32×52×311
Now multiplying the highest exponent prime factors to calculate the LCM of 6968 and 6975.
LCM(6968,6975) = 23×32×52×131×311×671
LCM(6968,6975) = 48601800
Factors of 6968
List of positive integer factors of 6968 that divides 6968 without a remainder.
1, 2, 4, 8, 13, 26, 52, 67, 104, 134, 268, 536, 871, 1742, 3484, 6968
Factors of 6975
List of positive integer factors of 6975 that divides 6975 without a remainder.
1, 3, 5, 9, 15, 25, 31, 45, 75, 93, 155, 225, 279, 465, 775, 1395, 2325, 6975
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6968 and 6975, than apply into the LCM equation.
GCF(6968,6975) = 1
LCM(6968,6975) = ( 6968 × 6975) / 1
LCM(6968,6975) = 48601800 / 1
LCM(6968,6975) = 48601800
(i) The LCM of 6975 and 6968 is associative
LCM of 6968 and 6975 = LCM of 6975 and 6968
1. What is the LCM of 6968 and 6975?
Answer: LCM of 6968 and 6975 is 48601800.
2. What are the Factors of 6968?
Answer: Factors of 6968 are 1, 2, 4, 8, 13, 26, 52, 67, 104, 134, 268, 536, 871, 1742, 3484, 6968. There are 16 integers that are factors of 6968. The greatest factor of 6968 is 6968.
3. What are the Factors of 6975?
Answer: Factors of 6975 are 1, 3, 5, 9, 15, 25, 31, 45, 75, 93, 155, 225, 279, 465, 775, 1395, 2325, 6975. There are 18 integers that are factors of 6975. The greatest factor of 6975 is 6975.
4. How to Find the LCM of 6968 and 6975?
Answer:
Least Common Multiple of 6968 and 6975 = 48601800
Step 1: Find the prime factorization of 6968
6968 = 2 x 2 x 2 x 13 x 67
Step 2: Find the prime factorization of 6975
6975 = 3 x 3 x 5 x 5 x 31
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 48601800 = 2 x 2 x 2 x 3 x 3 x 5 x 5 x 13 x 31 x 67
Step 4: Therefore, the least common multiple of 6968 and 6975 is 48601800.