Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 6209 and 6214 the smallest integer that is 38582726 that is divisible by both numbers.
Least Common Multiple (LCM) of 6209 and 6214 is 38582726.
LCM(6209,6214) = 38582726
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 6209 and 6214. First we will calculate the prime factors of 6209 and 6214.
Prime Factorization of 6209
7 | 6209 |
887 | 887 |
1 |
Prime factors of 6209 are 7,887. Prime factorization of 6209 in exponential form is:
6209 = 71×8871
Prime Factorization of 6214
2 | 6214 |
13 | 3107 |
239 | 239 |
1 |
Prime factors of 6214 are 2, 13,239. Prime factorization of 6214 in exponential form is:
6214 = 21×131×2391
Now multiplying the highest exponent prime factors to calculate the LCM of 6209 and 6214.
LCM(6209,6214) = 21×71×131×2391×8871
LCM(6209,6214) = 38582726
Factors of 6209
List of positive integer factors of 6209 that divides 6209 without a remainder.
1, 7, 887, 6209
Factors of 6214
List of positive integer factors of 6214 that divides 6214 without a remainder.
1, 2, 13, 26, 239, 478, 3107, 6214
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6209 and 6214, than apply into the LCM equation.
GCF(6209,6214) = 1
LCM(6209,6214) = ( 6209 × 6214) / 1
LCM(6209,6214) = 38582726 / 1
LCM(6209,6214) = 38582726
(i) The LCM of 6214 and 6209 is associative
LCM of 6209 and 6214 = LCM of 6214 and 6209
1. What is the LCM of 6209 and 6214?
Answer: LCM of 6209 and 6214 is 38582726.
2. What are the Factors of 6209?
Answer: Factors of 6209 are 1, 7, 887, 6209. There are 4 integers that are factors of 6209. The greatest factor of 6209 is 6209.
3. What are the Factors of 6214?
Answer: Factors of 6214 are 1, 2, 13, 26, 239, 478, 3107, 6214. There are 8 integers that are factors of 6214. The greatest factor of 6214 is 6214.
4. How to Find the LCM of 6209 and 6214?
Answer:
Least Common Multiple of 6209 and 6214 = 38582726
Step 1: Find the prime factorization of 6209
6209 = 7 x 887
Step 2: Find the prime factorization of 6214
6214 = 2 x 13 x 239
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 38582726 = 2 x 7 x 13 x 239 x 887
Step 4: Therefore, the least common multiple of 6209 and 6214 is 38582726.