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 6976 the smallest integer that is 6076096 that is divisible by both numbers.
Least Common Multiple (LCM) of 6968 and 6976 is 6076096.
LCM(6968,6976) = 6076096
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 6976. First we will calculate the prime factors of 6968 and 6976.
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 6976
2 | 6976 |
2 | 3488 |
2 | 1744 |
2 | 872 |
2 | 436 |
2 | 218 |
109 | 109 |
1 |
Prime factors of 6976 are 2,109. Prime factorization of 6976 in exponential form is:
6976 = 26×1091
Now multiplying the highest exponent prime factors to calculate the LCM of 6968 and 6976.
LCM(6968,6976) = 26×131×671×1091
LCM(6968,6976) = 6076096
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 6976
List of positive integer factors of 6976 that divides 6976 without a remainder.
1, 2, 4, 8, 16, 32, 64, 109, 218, 436, 872, 1744, 3488, 6976
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6968 and 6976, than apply into the LCM equation.
GCF(6968,6976) = 8
LCM(6968,6976) = ( 6968 × 6976) / 8
LCM(6968,6976) = 48608768 / 8
LCM(6968,6976) = 6076096
(i) The LCM of 6976 and 6968 is associative
LCM of 6968 and 6976 = LCM of 6976 and 6968
1. What is the LCM of 6968 and 6976?
Answer: LCM of 6968 and 6976 is 6076096.
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 6976?
Answer: Factors of 6976 are 1, 2, 4, 8, 16, 32, 64, 109, 218, 436, 872, 1744, 3488, 6976. There are 14 integers that are factors of 6976. The greatest factor of 6976 is 6976.
4. How to Find the LCM of 6968 and 6976?
Answer:
Least Common Multiple of 6968 and 6976 = 6076096
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 6976
6976 = 2 x 2 x 2 x 2 x 2 x 2 x 109
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 6076096 = 2 x 2 x 2 x 2 x 2 x 2 x 13 x 67 x 109
Step 4: Therefore, the least common multiple of 6968 and 6976 is 6076096.