Least Common Multiple of 204 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 204 and 212 the smallest integer that is 10812 that is divisible by both numbers.

Least Common Multiple (LCM) of 204 and 212 is 10812.

LCM(204,212) = 10812

LCM of 204 and 212

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

LCM of:
and

Least Common Multiple of 204 and 212

LCM of 204 and 212 is 10812

Least common multiple can be found by multiplying the highest exponent prime factors of 204 and 212. First we will calculate the prime factors of 204 and 212.

Prime Factorization of 204


2 204
2 102
3 51
17 17
1

Prime factors of 204 are 2, 3,17. Prime factorization of 204 in exponential form is:

204 = 22×31×171

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 204 and 212.

LCM(204,212) = 22×31×171×531
LCM(204,212) = 10812

Factors of 204

List of positive integer factors of 204 that divides 204 without a remainder.

1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204

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 204 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 204 and 212, than apply into the LCM equation.

GCF(204,212) = 4
LCM(204,212) = ( 204 × 212) / 4
LCM(204,212) = 43248 / 4
LCM(204,212) = 10812

Properties of LCM 204 and 212

(i) The LCM of 212 and 204 is associative

LCM of 204 and 212 = LCM of 212 and 204

Related Least Common Multiples of 204

Related Least Common Multiples of 212

Frequently Asked Questions on LCM of 204 and 212

1. What is the LCM of 204 and 212?

Answer: LCM of 204 and 212 is 10812.

2. What are the Factors of 204?

Answer: Factors of 204 are 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204. There are 12 integers that are factors of 204. The greatest factor of 204 is 204.

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 204 and 212?

Answer:

Least Common Multiple of 204 and 212 = 10812

Step 1: Find the prime factorization of 204

204 = 2 x 2 x 3 x 17

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 = 10812 = 2 x 2 x 3 x 17 x 53

Step 4: Therefore, the least common multiple of 204 and 212 is 10812.