Least Common Multiple of 209 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 209 and 212 the smallest integer that is 44308 that is divisible by both numbers.

Least Common Multiple (LCM) of 209 and 212 is 44308.

LCM(209,212) = 44308

LCM of 209 and 212

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

LCM of:
and

Least Common Multiple of 209 and 212

LCM of 209 and 212 is 44308

Least common multiple can be found by multiplying the highest exponent prime factors of 209 and 212. First we will calculate the prime factors of 209 and 212.

Prime Factorization of 209


11 209
19 19
1

Prime factors of 209 are 11,19. Prime factorization of 209 in exponential form is:

209 = 111×191

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 209 and 212.

LCM(209,212) = 22×111×191×531
LCM(209,212) = 44308

Factors of 209

List of positive integer factors of 209 that divides 209 without a remainder.

1, 11, 19, 209

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 209 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 209 and 212, than apply into the LCM equation.

GCF(209,212) = 1
LCM(209,212) = ( 209 × 212) / 1
LCM(209,212) = 44308 / 1
LCM(209,212) = 44308

Properties of LCM 209 and 212

(i) The LCM of 212 and 209 is associative

LCM of 209 and 212 = LCM of 212 and 209

Related Least Common Multiples of 209

Related Least Common Multiples of 212

Frequently Asked Questions on LCM of 209 and 212

1. What is the LCM of 209 and 212?

Answer: LCM of 209 and 212 is 44308.

2. What are the Factors of 209?

Answer: Factors of 209 are 1, 11, 19, 209. There are 4 integers that are factors of 209. The greatest factor of 209 is 209.

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 209 and 212?

Answer:

Least Common Multiple of 209 and 212 = 44308

Step 1: Find the prime factorization of 209

209 = 11 x 19

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 = 44308 = 2 x 2 x 11 x 19 x 53

Step 4: Therefore, the least common multiple of 209 and 212 is 44308.