Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 206 and 214 the smallest integer that is 22042 that is divisible by both numbers.
Least Common Multiple (LCM) of 206 and 214 is 22042.
LCM(206,214) = 22042
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 206 and 214. First we will calculate the prime factors of 206 and 214.
Prime Factorization of 206
2 | 206 |
103 | 103 |
1 |
Prime factors of 206 are 2,103. Prime factorization of 206 in exponential form is:
206 = 21×1031
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 206 and 214.
LCM(206,214) = 21×1031×1071
LCM(206,214) = 22042
Factors of 206
List of positive integer factors of 206 that divides 206 without a remainder.
1, 2, 103, 206
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 206 and 214, than apply into the LCM equation.
GCF(206,214) = 2
LCM(206,214) = ( 206 × 214) / 2
LCM(206,214) = 44084 / 2
LCM(206,214) = 22042
(i) The LCM of 214 and 206 is associative
LCM of 206 and 214 = LCM of 214 and 206
1. What is the LCM of 206 and 214?
Answer: LCM of 206 and 214 is 22042.
2. What are the Factors of 206?
Answer: Factors of 206 are 1, 2, 103, 206. There are 4 integers that are factors of 206. The greatest factor of 206 is 206.
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 206 and 214?
Answer:
Least Common Multiple of 206 and 214 = 22042
Step 1: Find the prime factorization of 206
206 = 2 x 103
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 = 22042 = 2 x 103 x 107
Step 4: Therefore, the least common multiple of 206 and 214 is 22042.