Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 6378 and 6384 the smallest integer that is 6786192 that is divisible by both numbers.
Least Common Multiple (LCM) of 6378 and 6384 is 6786192.
LCM(6378,6384) = 6786192
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 6378 and 6384. First we will calculate the prime factors of 6378 and 6384.
Prime Factorization of 6378
2 | 6378 |
3 | 3189 |
1063 | 1063 |
1 |
Prime factors of 6378 are 2, 3,1063. Prime factorization of 6378 in exponential form is:
6378 = 21×31×10631
Prime Factorization of 6384
2 | 6384 |
2 | 3192 |
2 | 1596 |
2 | 798 |
3 | 399 |
7 | 133 |
19 | 19 |
1 |
Prime factors of 6384 are 2, 3, 7,19. Prime factorization of 6384 in exponential form is:
6384 = 24×31×71×191
Now multiplying the highest exponent prime factors to calculate the LCM of 6378 and 6384.
LCM(6378,6384) = 24×31×71×191×10631
LCM(6378,6384) = 6786192
Factors of 6378
List of positive integer factors of 6378 that divides 6378 without a remainder.
1, 2, 3, 6, 1063, 2126, 3189, 6378
Factors of 6384
List of positive integer factors of 6384 that divides 6384 without a remainder.
1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 19, 21, 24, 28, 38, 42, 48, 56, 57, 76, 84, 112, 114, 133, 152, 168, 228, 266, 304, 336, 399, 456, 532, 798, 912, 1064, 1596, 2128, 3192, 6384
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6378 and 6384, than apply into the LCM equation.
GCF(6378,6384) = 6
LCM(6378,6384) = ( 6378 × 6384) / 6
LCM(6378,6384) = 40717152 / 6
LCM(6378,6384) = 6786192
(i) The LCM of 6384 and 6378 is associative
LCM of 6378 and 6384 = LCM of 6384 and 6378
1. What is the LCM of 6378 and 6384?
Answer: LCM of 6378 and 6384 is 6786192.
2. What are the Factors of 6378?
Answer: Factors of 6378 are 1, 2, 3, 6, 1063, 2126, 3189, 6378. There are 8 integers that are factors of 6378. The greatest factor of 6378 is 6378.
3. What are the Factors of 6384?
Answer: Factors of 6384 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 19, 21, 24, 28, 38, 42, 48, 56, 57, 76, 84, 112, 114, 133, 152, 168, 228, 266, 304, 336, 399, 456, 532, 798, 912, 1064, 1596, 2128, 3192, 6384. There are 40 integers that are factors of 6384. The greatest factor of 6384 is 6384.
4. How to Find the LCM of 6378 and 6384?
Answer:
Least Common Multiple of 6378 and 6384 = 6786192
Step 1: Find the prime factorization of 6378
6378 = 2 x 3 x 1063
Step 2: Find the prime factorization of 6384
6384 = 2 x 2 x 2 x 2 x 3 x 7 x 19
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 6786192 = 2 x 2 x 2 x 2 x 3 x 7 x 19 x 1063
Step 4: Therefore, the least common multiple of 6378 and 6384 is 6786192.