Least Common Multiple of 209 and 213
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 209 and 213 the smallest integer that is 44517 that is divisible by both numbers.
Least Common Multiple (LCM) of 209 and 213 is 44517.
LCM(209,213) = 44517
LCM of 209 and 213
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 209 and 213 by Prime method
- Least Common Multiple of 209 and 213 with GCF Formula
LCM of 209 and 213 is 44517
Least common multiple can be found by multiplying the highest exponent prime factors of 209 and 213. First we will calculate the prime factors of 209 and 213.
Prime Factorization of 209
| 11 | 209 |
| 19 | 19 |
| 1 |
Prime factors of 209 are 11,19. Prime factorization of 209 in exponential form is:
209 = 111×191
Prime Factorization of 213
| 3 | 213 |
| 71 | 71 |
| 1 |
Prime factors of 213 are 3,71. Prime factorization of 213 in exponential form is:
213 = 31×711
Now multiplying the highest exponent prime factors to calculate the LCM of 209 and 213.
LCM(209,213) = 31×111×191×711
LCM(209,213) = 44517
Factors of 209
List of positive integer factors of 209 that divides 209 without a remainder.
1, 11, 19, 209
Factors of 213
List of positive integer factors of 213 that divides 213 without a remainder.
1, 3, 71, 213
Least Common Multiple of 209 and 213 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 209 and 213, than apply into the LCM equation.
GCF(209,213) = 1
LCM(209,213) = ( 209 × 213) / 1
LCM(209,213) = 44517 / 1
LCM(209,213) = 44517
Properties of LCM 209 and 213
(i) The LCM of 213 and 209 is associative
LCM of 209 and 213 = LCM of 213 and 209
Related Least Common Multiples of 209
Related Least Common Multiples of 213
Frequently Asked Questions on LCM of 209 and 213
1. What is the LCM of 209 and 213?
Answer: LCM of 209 and 213 is 44517.
2. What are the Factors of 209?
Answer: Factors of 209 are 1, 11, 19, 209. There are 4 integers that are factors of 209. The greatest factor of 209 is 209.
3. What are the Factors of 213?
Answer: Factors of 213 are 1, 3, 71, 213. There are 4 integers that are factors of 213. The greatest factor of 213 is 213.
4. How to Find the LCM of 209 and 213?
Answer:
Least Common Multiple of 209 and 213 = 44517
Step 1: Find the prime factorization of 209
209 = 11 x 19
Step 2: Find the prime factorization of 213
213 = 3 x 71
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 44517 = 3 x 11 x 19 x 71
Step 4: Therefore, the least common multiple of 209 and 213 is 44517.