Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 864 and 866 the smallest integer that is 374112 that is divisible by both numbers.
Least Common Multiple (LCM) of 864 and 866 is 374112.
LCM(864,866) = 374112
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 864 and 866. First we will calculate the prime factors of 864 and 866.
Prime Factorization of 864
2 | 864 |
2 | 432 |
2 | 216 |
2 | 108 |
2 | 54 |
3 | 27 |
3 | 9 |
3 | 3 |
1 |
Prime factors of 864 are 2,3. Prime factorization of 864 in exponential form is:
864 = 25×33
Prime Factorization of 866
2 | 866 |
433 | 433 |
1 |
Prime factors of 866 are 2,433. Prime factorization of 866 in exponential form is:
866 = 21×4331
Now multiplying the highest exponent prime factors to calculate the LCM of 864 and 866.
LCM(864,866) = 25×33×4331
LCM(864,866) = 374112
Factors of 864
List of positive integer factors of 864 that divides 864 without a remainder.
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 96, 108, 144, 216, 288, 432, 864
Factors of 866
List of positive integer factors of 866 that divides 866 without a remainder.
1, 2, 433, 866
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 864 and 866, than apply into the LCM equation.
GCF(864,866) = 2
LCM(864,866) = ( 864 × 866) / 2
LCM(864,866) = 748224 / 2
LCM(864,866) = 374112
(i) The LCM of 866 and 864 is associative
LCM of 864 and 866 = LCM of 866 and 864
1. What is the LCM of 864 and 866?
Answer: LCM of 864 and 866 is 374112.
2. What are the Factors of 864?
Answer: Factors of 864 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 96, 108, 144, 216, 288, 432, 864. There are 24 integers that are factors of 864. The greatest factor of 864 is 864.
3. What are the Factors of 866?
Answer: Factors of 866 are 1, 2, 433, 866. There are 4 integers that are factors of 866. The greatest factor of 866 is 866.
4. How to Find the LCM of 864 and 866?
Answer:
Least Common Multiple of 864 and 866 = 374112
Step 1: Find the prime factorization of 864
864 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3
Step 2: Find the prime factorization of 866
866 = 2 x 433
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 374112 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 433
Step 4: Therefore, the least common multiple of 864 and 866 is 374112.