Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 8211 and 8214 the smallest integer that is 22481718 that is divisible by both numbers.
Least Common Multiple (LCM) of 8211 and 8214 is 22481718.
LCM(8211,8214) = 22481718
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 8211 and 8214. First we will calculate the prime factors of 8211 and 8214.
Prime Factorization of 8211
3 | 8211 |
7 | 2737 |
17 | 391 |
23 | 23 |
1 |
Prime factors of 8211 are 3, 7, 17,23. Prime factorization of 8211 in exponential form is:
8211 = 31×71×171×231
Prime Factorization of 8214
2 | 8214 |
3 | 4107 |
37 | 1369 |
37 | 37 |
1 |
Prime factors of 8214 are 2, 3,37. Prime factorization of 8214 in exponential form is:
8214 = 21×31×372
Now multiplying the highest exponent prime factors to calculate the LCM of 8211 and 8214.
LCM(8211,8214) = 21×31×71×171×231×372
LCM(8211,8214) = 22481718
Factors of 8211
List of positive integer factors of 8211 that divides 8211 without a remainder.
1, 3, 7, 17, 21, 23, 51, 69, 119, 161, 357, 391, 483, 1173, 2737, 8211
Factors of 8214
List of positive integer factors of 8214 that divides 8214 without a remainder.
1, 2, 3, 6, 37, 74, 111, 222, 1369, 2738, 4107, 8214
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8211 and 8214, than apply into the LCM equation.
GCF(8211,8214) = 3
LCM(8211,8214) = ( 8211 × 8214) / 3
LCM(8211,8214) = 67445154 / 3
LCM(8211,8214) = 22481718
(i) The LCM of 8214 and 8211 is associative
LCM of 8211 and 8214 = LCM of 8214 and 8211
1. What is the LCM of 8211 and 8214?
Answer: LCM of 8211 and 8214 is 22481718.
2. What are the Factors of 8211?
Answer: Factors of 8211 are 1, 3, 7, 17, 21, 23, 51, 69, 119, 161, 357, 391, 483, 1173, 2737, 8211. There are 16 integers that are factors of 8211. The greatest factor of 8211 is 8211.
3. What are the Factors of 8214?
Answer: Factors of 8214 are 1, 2, 3, 6, 37, 74, 111, 222, 1369, 2738, 4107, 8214. There are 12 integers that are factors of 8214. The greatest factor of 8214 is 8214.
4. How to Find the LCM of 8211 and 8214?
Answer:
Least Common Multiple of 8211 and 8214 = 22481718
Step 1: Find the prime factorization of 8211
8211 = 3 x 7 x 17 x 23
Step 2: Find the prime factorization of 8214
8214 = 2 x 3 x 37 x 37
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 22481718 = 2 x 3 x 7 x 17 x 23 x 37 x 37
Step 4: Therefore, the least common multiple of 8211 and 8214 is 22481718.