Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 6308 and 6314 the smallest integer that is 19914356 that is divisible by both numbers.
Least Common Multiple (LCM) of 6308 and 6314 is 19914356.
LCM(6308,6314) = 19914356
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 6308 and 6314. First we will calculate the prime factors of 6308 and 6314.
Prime Factorization of 6308
2 | 6308 |
2 | 3154 |
19 | 1577 |
83 | 83 |
1 |
Prime factors of 6308 are 2, 19,83. Prime factorization of 6308 in exponential form is:
6308 = 22×191×831
Prime Factorization of 6314
2 | 6314 |
7 | 3157 |
11 | 451 |
41 | 41 |
1 |
Prime factors of 6314 are 2, 7, 11,41. Prime factorization of 6314 in exponential form is:
6314 = 21×71×111×411
Now multiplying the highest exponent prime factors to calculate the LCM of 6308 and 6314.
LCM(6308,6314) = 22×71×111×191×411×831
LCM(6308,6314) = 19914356
Factors of 6308
List of positive integer factors of 6308 that divides 6308 without a remainder.
1, 2, 4, 19, 38, 76, 83, 166, 332, 1577, 3154, 6308
Factors of 6314
List of positive integer factors of 6314 that divides 6314 without a remainder.
1, 2, 7, 11, 14, 22, 41, 77, 82, 154, 287, 451, 574, 902, 3157, 6314
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6308 and 6314, than apply into the LCM equation.
GCF(6308,6314) = 2
LCM(6308,6314) = ( 6308 × 6314) / 2
LCM(6308,6314) = 39828712 / 2
LCM(6308,6314) = 19914356
(i) The LCM of 6314 and 6308 is associative
LCM of 6308 and 6314 = LCM of 6314 and 6308
1. What is the LCM of 6308 and 6314?
Answer: LCM of 6308 and 6314 is 19914356.
2. What are the Factors of 6308?
Answer: Factors of 6308 are 1, 2, 4, 19, 38, 76, 83, 166, 332, 1577, 3154, 6308. There are 12 integers that are factors of 6308. The greatest factor of 6308 is 6308.
3. What are the Factors of 6314?
Answer: Factors of 6314 are 1, 2, 7, 11, 14, 22, 41, 77, 82, 154, 287, 451, 574, 902, 3157, 6314. There are 16 integers that are factors of 6314. The greatest factor of 6314 is 6314.
4. How to Find the LCM of 6308 and 6314?
Answer:
Least Common Multiple of 6308 and 6314 = 19914356
Step 1: Find the prime factorization of 6308
6308 = 2 x 2 x 19 x 83
Step 2: Find the prime factorization of 6314
6314 = 2 x 7 x 11 x 41
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 19914356 = 2 x 2 x 7 x 11 x 19 x 41 x 83
Step 4: Therefore, the least common multiple of 6308 and 6314 is 19914356.