Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 8214 and 8221 the smallest integer that is 67527294 that is divisible by both numbers.
Least Common Multiple (LCM) of 8214 and 8221 is 67527294.
LCM(8214,8221) = 67527294
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 8214 and 8221. First we will calculate the prime factors of 8214 and 8221.
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
Prime Factorization of 8221
8221 | 8221 |
1 |
Prime factors of 8221 are 8221. Prime factorization of 8221 in exponential form is:
8221 = 82211
Now multiplying the highest exponent prime factors to calculate the LCM of 8214 and 8221.
LCM(8214,8221) = 21×31×372×82211
LCM(8214,8221) = 67527294
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
Factors of 8221
List of positive integer factors of 8221 that divides 8221 without a remainder.
1, 8221
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8214 and 8221, than apply into the LCM equation.
GCF(8214,8221) = 1
LCM(8214,8221) = ( 8214 × 8221) / 1
LCM(8214,8221) = 67527294 / 1
LCM(8214,8221) = 67527294
(i) The LCM of 8221 and 8214 is associative
LCM of 8214 and 8221 = LCM of 8221 and 8214
1. What is the LCM of 8214 and 8221?
Answer: LCM of 8214 and 8221 is 67527294.
2. 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.
3. What are the Factors of 8221?
Answer: Factors of 8221 are 1, 8221. There are 2 integers that are factors of 8221. The greatest factor of 8221 is 8221.
4. How to Find the LCM of 8214 and 8221?
Answer:
Least Common Multiple of 8214 and 8221 = 67527294
Step 1: Find the prime factorization of 8214
8214 = 2 x 3 x 37 x 37
Step 2: Find the prime factorization of 8221
8221 = 8221
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 67527294 = 2 x 3 x 37 x 37 x 8221
Step 4: Therefore, the least common multiple of 8214 and 8221 is 67527294.