Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 891 and 896 the smallest integer that is 798336 that is divisible by both numbers.
Least Common Multiple (LCM) of 891 and 896 is 798336.
LCM(891,896) = 798336
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 891 and 896. First we will calculate the prime factors of 891 and 896.
Prime Factorization of 891
3 | 891 |
3 | 297 |
3 | 99 |
3 | 33 |
11 | 11 |
1 |
Prime factors of 891 are 3,11. Prime factorization of 891 in exponential form is:
891 = 34×111
Prime Factorization of 896
2 | 896 |
2 | 448 |
2 | 224 |
2 | 112 |
2 | 56 |
2 | 28 |
2 | 14 |
7 | 7 |
1 |
Prime factors of 896 are 2,7. Prime factorization of 896 in exponential form is:
896 = 27×71
Now multiplying the highest exponent prime factors to calculate the LCM of 891 and 896.
LCM(891,896) = 27×34×71×111
LCM(891,896) = 798336
Factors of 891
List of positive integer factors of 891 that divides 891 without a remainder.
1, 3, 9, 11, 27, 33, 81, 99, 297, 891
Factors of 896
List of positive integer factors of 896 that divides 896 without a remainder.
1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 128, 224, 448, 896
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 891 and 896, than apply into the LCM equation.
GCF(891,896) = 1
LCM(891,896) = ( 891 × 896) / 1
LCM(891,896) = 798336 / 1
LCM(891,896) = 798336
(i) The LCM of 896 and 891 is associative
LCM of 891 and 896 = LCM of 896 and 891
1. What is the LCM of 891 and 896?
Answer: LCM of 891 and 896 is 798336.
2. What are the Factors of 891?
Answer: Factors of 891 are 1, 3, 9, 11, 27, 33, 81, 99, 297, 891. There are 10 integers that are factors of 891. The greatest factor of 891 is 891.
3. What are the Factors of 896?
Answer: Factors of 896 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 128, 224, 448, 896. There are 16 integers that are factors of 896. The greatest factor of 896 is 896.
4. How to Find the LCM of 891 and 896?
Answer:
Least Common Multiple of 891 and 896 = 798336
Step 1: Find the prime factorization of 891
891 = 3 x 3 x 3 x 3 x 11
Step 2: Find the prime factorization of 896
896 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 7
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 798336 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 7 x 11
Step 4: Therefore, the least common multiple of 891 and 896 is 798336.