Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 213 and 214 the smallest integer that is 45582 that is divisible by both numbers.
Least Common Multiple (LCM) of 213 and 214 is 45582.
LCM(213,214) = 45582
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 213 and 214. First we will calculate the prime factors of 213 and 214.
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
Prime Factorization of 214
2 | 214 |
107 | 107 |
1 |
Prime factors of 214 are 2,107. Prime factorization of 214 in exponential form is:
214 = 21×1071
Now multiplying the highest exponent prime factors to calculate the LCM of 213 and 214.
LCM(213,214) = 21×31×711×1071
LCM(213,214) = 45582
Factors of 213
List of positive integer factors of 213 that divides 213 without a remainder.
1, 3, 71, 213
Factors of 214
List of positive integer factors of 214 that divides 214 without a remainder.
1, 2, 107, 214
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 213 and 214, than apply into the LCM equation.
GCF(213,214) = 1
LCM(213,214) = ( 213 × 214) / 1
LCM(213,214) = 45582 / 1
LCM(213,214) = 45582
(i) The LCM of 214 and 213 is associative
LCM of 213 and 214 = LCM of 214 and 213
1. What is the LCM of 213 and 214?
Answer: LCM of 213 and 214 is 45582.
2. 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.
3. What are the Factors of 214?
Answer: Factors of 214 are 1, 2, 107, 214. There are 4 integers that are factors of 214. The greatest factor of 214 is 214.
4. How to Find the LCM of 213 and 214?
Answer:
Least Common Multiple of 213 and 214 = 45582
Step 1: Find the prime factorization of 213
213 = 3 x 71
Step 2: Find the prime factorization of 214
214 = 2 x 107
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 45582 = 2 x 3 x 71 x 107
Step 4: Therefore, the least common multiple of 213 and 214 is 45582.