Least Common Multiple of 4209 and 4214
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 4209 and 4214 the smallest integer that is 17736726 that is divisible by both numbers.
Least Common Multiple (LCM) of 4209 and 4214 is 17736726.
LCM(4209,4214) = 17736726
LCM of 4209 and 4214
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 4209 and 4214 by Prime method
- Least Common Multiple of 4209 and 4214 with GCF Formula
LCM of 4209 and 4214 is 17736726
Least common multiple can be found by multiplying the highest exponent prime factors of 4209 and 4214. First we will calculate the prime factors of 4209 and 4214.
Prime Factorization of 4209
| 3 | 4209 |
| 23 | 1403 |
| 61 | 61 |
| 1 |
Prime factors of 4209 are 3, 23,61. Prime factorization of 4209 in exponential form is:
4209 = 31×231×611
Prime Factorization of 4214
| 2 | 4214 |
| 7 | 2107 |
| 7 | 301 |
| 43 | 43 |
| 1 |
Prime factors of 4214 are 2, 7,43. Prime factorization of 4214 in exponential form is:
4214 = 21×72×431
Now multiplying the highest exponent prime factors to calculate the LCM of 4209 and 4214.
LCM(4209,4214) = 21×31×72×231×431×611
LCM(4209,4214) = 17736726
Factors of 4209
List of positive integer factors of 4209 that divides 4209 without a remainder.
1, 3, 23, 61, 69, 183, 1403, 4209
Factors of 4214
List of positive integer factors of 4214 that divides 4214 without a remainder.
1, 2, 7, 14, 43, 49, 86, 98, 301, 602, 2107, 4214
Least Common Multiple of 4209 and 4214 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 4209 and 4214, than apply into the LCM equation.
GCF(4209,4214) = 1
LCM(4209,4214) = ( 4209 × 4214) / 1
LCM(4209,4214) = 17736726 / 1
LCM(4209,4214) = 17736726
Properties of LCM 4209 and 4214
(i) The LCM of 4214 and 4209 is associative
LCM of 4209 and 4214 = LCM of 4214 and 4209
Related Least Common Multiples of 4209
Related Least Common Multiples of 4214
Frequently Asked Questions on LCM of 4209 and 4214
1. What is the LCM of 4209 and 4214?
Answer: LCM of 4209 and 4214 is 17736726.
2. What are the Factors of 4209?
Answer: Factors of 4209 are 1, 3, 23, 61, 69, 183, 1403, 4209. There are 8 integers that are factors of 4209. The greatest factor of 4209 is 4209.
3. What are the Factors of 4214?
Answer: Factors of 4214 are 1, 2, 7, 14, 43, 49, 86, 98, 301, 602, 2107, 4214. There are 12 integers that are factors of 4214. The greatest factor of 4214 is 4214.
4. How to Find the LCM of 4209 and 4214?
Answer:
Least Common Multiple of 4209 and 4214 = 17736726
Step 1: Find the prime factorization of 4209
4209 = 3 x 23 x 61
Step 2: Find the prime factorization of 4214
4214 = 2 x 7 x 7 x 43
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 17736726 = 2 x 3 x 7 x 7 x 23 x 43 x 61
Step 4: Therefore, the least common multiple of 4209 and 4214 is 17736726.