Least Common Multiple of 209 and 210

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 210 the smallest integer that is 43890 that is divisible by both numbers.

Least Common Multiple (LCM) of 209 and 210 is 43890.

LCM(209,210) = 43890

LCM of 209 and 210

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

LCM of:
and

Least Common Multiple of 209 and 210

LCM of 209 and 210 is 43890

Least common multiple can be found by multiplying the highest exponent prime factors of 209 and 210. First we will calculate the prime factors of 209 and 210.

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 210


2 210
3 105
5 35
7 7
1

Prime factors of 210 are 2, 3, 5,7. Prime factorization of 210 in exponential form is:

210 = 21×31×51×71

Now multiplying the highest exponent prime factors to calculate the LCM of 209 and 210.

LCM(209,210) = 21×31×51×71×111×191
LCM(209,210) = 43890

Factors of 209

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

1, 11, 19, 209

Factors of 210

List of positive integer factors of 210 that divides 210 without a remainder.

1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210

Least Common Multiple of 209 and 210 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 210, than apply into the LCM equation.

GCF(209,210) = 1
LCM(209,210) = ( 209 × 210) / 1
LCM(209,210) = 43890 / 1
LCM(209,210) = 43890

Properties of LCM 209 and 210

(i) The LCM of 210 and 209 is associative

LCM of 209 and 210 = LCM of 210 and 209

Related Least Common Multiples of 209

Related Least Common Multiples of 210

Frequently Asked Questions on LCM of 209 and 210

1. What is the LCM of 209 and 210?

Answer: LCM of 209 and 210 is 43890.

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 210?

Answer: Factors of 210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210. There are 16 integers that are factors of 210. The greatest factor of 210 is 210.

4. How to Find the LCM of 209 and 210?

Answer:

Least Common Multiple of 209 and 210 = 43890

Step 1: Find the prime factorization of 209

209 = 11 x 19

Step 2: Find the prime factorization of 210

210 = 2 x 3 x 5 x 7

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 43890 = 2 x 3 x 5 x 7 x 11 x 19

Step 4: Therefore, the least common multiple of 209 and 210 is 43890.