Least Common Multiple of 205 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 205 and 210 the smallest integer that is 8610 that is divisible by both numbers.

Least Common Multiple (LCM) of 205 and 210 is 8610.

LCM(205,210) = 8610

LCM of 205 and 210

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

LCM of:
and

Least Common Multiple of 205 and 210

LCM of 205 and 210 is 8610

Least common multiple can be found by multiplying the highest exponent prime factors of 205 and 210. First we will calculate the prime factors of 205 and 210.

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 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 205 and 210.

LCM(205,210) = 21×31×51×71×411
LCM(205,210) = 8610

Factors of 205

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

1, 5, 41, 205

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 205 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 205 and 210, than apply into the LCM equation.

GCF(205,210) = 5
LCM(205,210) = ( 205 × 210) / 5
LCM(205,210) = 43050 / 5
LCM(205,210) = 8610

Properties of LCM 205 and 210

(i) The LCM of 210 and 205 is associative

LCM of 205 and 210 = LCM of 210 and 205

Related Least Common Multiples of 205

Related Least Common Multiples of 210

Frequently Asked Questions on LCM of 205 and 210

1. What is the LCM of 205 and 210?

Answer: LCM of 205 and 210 is 8610.

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 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 205 and 210?

Answer:

Least Common Multiple of 205 and 210 = 8610

Step 1: Find the prime factorization of 205

205 = 5 x 41

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 = 8610 = 2 x 3 x 5 x 7 x 41

Step 4: Therefore, the least common multiple of 205 and 210 is 8610.