Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 207 and 212 the smallest integer that is 43884 that is divisible by both numbers.
Least Common Multiple (LCM) of 207 and 212 is 43884.
LCM(207,212) = 43884
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 207 and 212. First we will calculate the prime factors of 207 and 212.
Prime Factorization of 207
3 | 207 |
3 | 69 |
23 | 23 |
1 |
Prime factors of 207 are 3,23. Prime factorization of 207 in exponential form is:
207 = 32×231
Prime Factorization of 212
2 | 212 |
2 | 106 |
53 | 53 |
1 |
Prime factors of 212 are 2,53. Prime factorization of 212 in exponential form is:
212 = 22×531
Now multiplying the highest exponent prime factors to calculate the LCM of 207 and 212.
LCM(207,212) = 22×32×231×531
LCM(207,212) = 43884
Factors of 207
List of positive integer factors of 207 that divides 207 without a remainder.
1, 3, 9, 23, 69, 207
Factors of 212
List of positive integer factors of 212 that divides 212 without a remainder.
1, 2, 4, 53, 106, 212
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 207 and 212, than apply into the LCM equation.
GCF(207,212) = 1
LCM(207,212) = ( 207 × 212) / 1
LCM(207,212) = 43884 / 1
LCM(207,212) = 43884
(i) The LCM of 212 and 207 is associative
LCM of 207 and 212 = LCM of 212 and 207
1. What is the LCM of 207 and 212?
Answer: LCM of 207 and 212 is 43884.
2. What are the Factors of 207?
Answer: Factors of 207 are 1, 3, 9, 23, 69, 207. There are 6 integers that are factors of 207. The greatest factor of 207 is 207.
3. What are the Factors of 212?
Answer: Factors of 212 are 1, 2, 4, 53, 106, 212. There are 6 integers that are factors of 212. The greatest factor of 212 is 212.
4. How to Find the LCM of 207 and 212?
Answer:
Least Common Multiple of 207 and 212 = 43884
Step 1: Find the prime factorization of 207
207 = 3 x 3 x 23
Step 2: Find the prime factorization of 212
212 = 2 x 2 x 53
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 43884 = 2 x 2 x 3 x 3 x 23 x 53
Step 4: Therefore, the least common multiple of 207 and 212 is 43884.