Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 8206 and 8214 the smallest integer that is 33702042 that is divisible by both numbers.
Least Common Multiple (LCM) of 8206 and 8214 is 33702042.
LCM(8206,8214) = 33702042
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 8206 and 8214. First we will calculate the prime factors of 8206 and 8214.
Prime Factorization of 8206
2 | 8206 |
11 | 4103 |
373 | 373 |
1 |
Prime factors of 8206 are 2, 11,373. Prime factorization of 8206 in exponential form is:
8206 = 21×111×3731
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 8206 and 8214.
LCM(8206,8214) = 21×31×111×372×3731
LCM(8206,8214) = 33702042
Factors of 8206
List of positive integer factors of 8206 that divides 8206 without a remainder.
1, 2, 11, 22, 373, 746, 4103, 8206
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 8206 and 8214, than apply into the LCM equation.
GCF(8206,8214) = 2
LCM(8206,8214) = ( 8206 × 8214) / 2
LCM(8206,8214) = 67404084 / 2
LCM(8206,8214) = 33702042
(i) The LCM of 8214 and 8206 is associative
LCM of 8206 and 8214 = LCM of 8214 and 8206
1. What is the LCM of 8206 and 8214?
Answer: LCM of 8206 and 8214 is 33702042.
2. What are the Factors of 8206?
Answer: Factors of 8206 are 1, 2, 11, 22, 373, 746, 4103, 8206. There are 8 integers that are factors of 8206. The greatest factor of 8206 is 8206.
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 8206 and 8214?
Answer:
Least Common Multiple of 8206 and 8214 = 33702042
Step 1: Find the prime factorization of 8206
8206 = 2 x 11 x 373
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 = 33702042 = 2 x 3 x 11 x 37 x 37 x 373
Step 4: Therefore, the least common multiple of 8206 and 8214 is 33702042.