Least Common Multiple of 205 and 212

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 212 the smallest integer that is 43460 that is divisible by both numbers.

Least Common Multiple (LCM) of 205 and 212 is 43460.

LCM(205,212) = 43460

LCM of 205 and 212

Least common multiple or lowest common denominator (LCD) can be calculated in three ways;

LCM of:
and

Least Common Multiple of 205 and 212

LCM of 205 and 212 is 43460

Least common multiple can be found by multiplying the highest exponent prime factors of 205 and 212. First we will calculate the prime factors of 205 and 212.

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 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 205 and 212.

LCM(205,212) = 22×51×411×531
LCM(205,212) = 43460

Factors of 205

List of positive integer factors of 205 that divides 205 without a remainder.

1, 5, 41, 205

Factors of 212

List of positive integer factors of 212 that divides 212 without a remainder.

1, 2, 4, 53, 106, 212

Least Common Multiple of 205 and 212 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 205 and 212, than apply into the LCM equation.

GCF(205,212) = 1
LCM(205,212) = ( 205 × 212) / 1
LCM(205,212) = 43460 / 1
LCM(205,212) = 43460

Properties of LCM 205 and 212

(i) The LCM of 212 and 205 is associative

LCM of 205 and 212 = LCM of 212 and 205

Related Least Common Multiples of 205

Related Least Common Multiples of 212

Frequently Asked Questions on LCM of 205 and 212

1. What is the LCM of 205 and 212?

Answer: LCM of 205 and 212 is 43460.

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 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 205 and 212?

Answer:

Least Common Multiple of 205 and 212 = 43460

Step 1: Find the prime factorization of 205

205 = 5 x 41

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 = 43460 = 2 x 2 x 5 x 41 x 53

Step 4: Therefore, the least common multiple of 205 and 212 is 43460.