Least Common Multiple of 209 and 214

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 214 the smallest integer that is 44726 that is divisible by both numbers.

Least Common Multiple (LCM) of 209 and 214 is 44726.

LCM(209,214) = 44726

LCM of 209 and 214

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

LCM of:
and

Least Common Multiple of 209 and 214

LCM of 209 and 214 is 44726

Least common multiple can be found by multiplying the highest exponent prime factors of 209 and 214. First we will calculate the prime factors of 209 and 214.

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 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 209 and 214.

LCM(209,214) = 21×111×191×1071
LCM(209,214) = 44726

Factors of 209

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

1, 11, 19, 209

Factors of 214

List of positive integer factors of 214 that divides 214 without a remainder.

1, 2, 107, 214

Least Common Multiple of 209 and 214 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 214, than apply into the LCM equation.

GCF(209,214) = 1
LCM(209,214) = ( 209 × 214) / 1
LCM(209,214) = 44726 / 1
LCM(209,214) = 44726

Properties of LCM 209 and 214

(i) The LCM of 214 and 209 is associative

LCM of 209 and 214 = LCM of 214 and 209

Related Least Common Multiples of 209

Related Least Common Multiples of 214

Frequently Asked Questions on LCM of 209 and 214

1. What is the LCM of 209 and 214?

Answer: LCM of 209 and 214 is 44726.

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 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 209 and 214?

Answer:

Least Common Multiple of 209 and 214 = 44726

Step 1: Find the prime factorization of 209

209 = 11 x 19

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 = 44726 = 2 x 11 x 19 x 107

Step 4: Therefore, the least common multiple of 209 and 214 is 44726.