Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 6780 and 6786 the smallest integer that is 7668180 that is divisible by both numbers.
Least Common Multiple (LCM) of 6780 and 6786 is 7668180.
LCM(6780,6786) = 7668180
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 6780 and 6786. First we will calculate the prime factors of 6780 and 6786.
Prime Factorization of 6780
2 | 6780 |
2 | 3390 |
3 | 1695 |
5 | 565 |
113 | 113 |
1 |
Prime factors of 6780 are 2, 3, 5,113. Prime factorization of 6780 in exponential form is:
6780 = 22×31×51×1131
Prime Factorization of 6786
2 | 6786 |
3 | 3393 |
3 | 1131 |
13 | 377 |
29 | 29 |
1 |
Prime factors of 6786 are 2, 3, 13,29. Prime factorization of 6786 in exponential form is:
6786 = 21×32×131×291
Now multiplying the highest exponent prime factors to calculate the LCM of 6780 and 6786.
LCM(6780,6786) = 22×32×51×131×291×1131
LCM(6780,6786) = 7668180
Factors of 6780
List of positive integer factors of 6780 that divides 6780 without a remainder.
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 113, 226, 339, 452, 565, 678, 1130, 1356, 1695, 2260, 3390, 6780
Factors of 6786
List of positive integer factors of 6786 that divides 6786 without a remainder.
1, 2, 3, 6, 9, 13, 18, 26, 29, 39, 58, 78, 87, 117, 174, 234, 261, 377, 522, 754, 1131, 2262, 3393, 6786
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6780 and 6786, than apply into the LCM equation.
GCF(6780,6786) = 6
LCM(6780,6786) = ( 6780 × 6786) / 6
LCM(6780,6786) = 46009080 / 6
LCM(6780,6786) = 7668180
(i) The LCM of 6786 and 6780 is associative
LCM of 6780 and 6786 = LCM of 6786 and 6780
1. What is the LCM of 6780 and 6786?
Answer: LCM of 6780 and 6786 is 7668180.
2. What are the Factors of 6780?
Answer: Factors of 6780 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 113, 226, 339, 452, 565, 678, 1130, 1356, 1695, 2260, 3390, 6780. There are 24 integers that are factors of 6780. The greatest factor of 6780 is 6780.
3. What are the Factors of 6786?
Answer: Factors of 6786 are 1, 2, 3, 6, 9, 13, 18, 26, 29, 39, 58, 78, 87, 117, 174, 234, 261, 377, 522, 754, 1131, 2262, 3393, 6786. There are 24 integers that are factors of 6786. The greatest factor of 6786 is 6786.
4. How to Find the LCM of 6780 and 6786?
Answer:
Least Common Multiple of 6780 and 6786 = 7668180
Step 1: Find the prime factorization of 6780
6780 = 2 x 2 x 3 x 5 x 113
Step 2: Find the prime factorization of 6786
6786 = 2 x 3 x 3 x 13 x 29
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 7668180 = 2 x 2 x 3 x 3 x 5 x 13 x 29 x 113
Step 4: Therefore, the least common multiple of 6780 and 6786 is 7668180.