Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 6906 and 6912 the smallest integer that is 7955712 that is divisible by both numbers.
Least Common Multiple (LCM) of 6906 and 6912 is 7955712.
LCM(6906,6912) = 7955712
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 6906 and 6912. First we will calculate the prime factors of 6906 and 6912.
Prime Factorization of 6906
2 | 6906 |
3 | 3453 |
1151 | 1151 |
1 |
Prime factors of 6906 are 2, 3,1151. Prime factorization of 6906 in exponential form is:
6906 = 21×31×11511
Prime Factorization of 6912
2 | 6912 |
2 | 3456 |
2 | 1728 |
2 | 864 |
2 | 432 |
2 | 216 |
2 | 108 |
2 | 54 |
3 | 27 |
3 | 9 |
3 | 3 |
1 |
Prime factors of 6912 are 2,3. Prime factorization of 6912 in exponential form is:
6912 = 28×33
Now multiplying the highest exponent prime factors to calculate the LCM of 6906 and 6912.
LCM(6906,6912) = 28×33×11511
LCM(6906,6912) = 7955712
Factors of 6906
List of positive integer factors of 6906 that divides 6906 without a remainder.
1, 2, 3, 6, 1151, 2302, 3453, 6906
Factors of 6912
List of positive integer factors of 6912 that divides 6912 without a remainder.
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 128, 144, 192, 216, 256, 288, 384, 432, 576, 768, 864, 1152, 1728, 2304, 3456, 6912
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6906 and 6912, than apply into the LCM equation.
GCF(6906,6912) = 6
LCM(6906,6912) = ( 6906 × 6912) / 6
LCM(6906,6912) = 47734272 / 6
LCM(6906,6912) = 7955712
(i) The LCM of 6912 and 6906 is associative
LCM of 6906 and 6912 = LCM of 6912 and 6906
1. What is the LCM of 6906 and 6912?
Answer: LCM of 6906 and 6912 is 7955712.
2. What are the Factors of 6906?
Answer: Factors of 6906 are 1, 2, 3, 6, 1151, 2302, 3453, 6906. There are 8 integers that are factors of 6906. The greatest factor of 6906 is 6906.
3. What are the Factors of 6912?
Answer: Factors of 6912 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 128, 144, 192, 216, 256, 288, 384, 432, 576, 768, 864, 1152, 1728, 2304, 3456, 6912. There are 36 integers that are factors of 6912. The greatest factor of 6912 is 6912.
4. How to Find the LCM of 6906 and 6912?
Answer:
Least Common Multiple of 6906 and 6912 = 7955712
Step 1: Find the prime factorization of 6906
6906 = 2 x 3 x 1151
Step 2: Find the prime factorization of 6912
6912 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 7955712 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 1151
Step 4: Therefore, the least common multiple of 6906 and 6912 is 7955712.