Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 205 and 213 the smallest integer that is 43665 that is divisible by both numbers.
Least Common Multiple (LCM) of 205 and 213 is 43665.
LCM(205,213) = 43665
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 205 and 213. First we will calculate the prime factors of 205 and 213.
Prime Factorization of 205
5 | 205 |
41 | 41 |
1 |
Prime factors of 205 are 5,41. Prime factorization of 205 in exponential form is:
205 = 51×411
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 205 and 213.
LCM(205,213) = 31×51×411×711
LCM(205,213) = 43665
Factors of 205
List of positive integer factors of 205 that divides 205 without a remainder.
1, 5, 41, 205
Factors of 213
List of positive integer factors of 213 that divides 213 without a remainder.
1, 3, 71, 213
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 205 and 213, than apply into the LCM equation.
GCF(205,213) = 1
LCM(205,213) = ( 205 × 213) / 1
LCM(205,213) = 43665 / 1
LCM(205,213) = 43665
(i) The LCM of 213 and 205 is associative
LCM of 205 and 213 = LCM of 213 and 205
1. What is the LCM of 205 and 213?
Answer: LCM of 205 and 213 is 43665.
2. What are the Factors of 205?
Answer: Factors of 205 are 1, 5, 41, 205. There are 4 integers that are factors of 205. The greatest factor of 205 is 205.
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 205 and 213?
Answer:
Least Common Multiple of 205 and 213 = 43665
Step 1: Find the prime factorization of 205
205 = 5 x 41
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 = 43665 = 3 x 5 x 41 x 71
Step 4: Therefore, the least common multiple of 205 and 213 is 43665.