Least Common Multiple of 204 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 204 and 210 the smallest integer that is 7140 that is divisible by both numbers.

Least Common Multiple (LCM) of 204 and 210 is 7140.

LCM(204,210) = 7140

LCM of 204 and 210

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

LCM of:
and

Least Common Multiple of 204 and 210

LCM of 204 and 210 is 7140

Least common multiple can be found by multiplying the highest exponent prime factors of 204 and 210. First we will calculate the prime factors of 204 and 210.

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 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 204 and 210.

LCM(204,210) = 22×31×51×71×171
LCM(204,210) = 7140

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 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 204 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 204 and 210, than apply into the LCM equation.

GCF(204,210) = 6
LCM(204,210) = ( 204 × 210) / 6
LCM(204,210) = 42840 / 6
LCM(204,210) = 7140

Properties of LCM 204 and 210

(i) The LCM of 210 and 204 is associative

LCM of 204 and 210 = LCM of 210 and 204

Related Least Common Multiples of 204

Related Least Common Multiples of 210

Frequently Asked Questions on LCM of 204 and 210

1. What is the LCM of 204 and 210?

Answer: LCM of 204 and 210 is 7140.

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 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 204 and 210?

Answer:

Least Common Multiple of 204 and 210 = 7140

Step 1: Find the prime factorization of 204

204 = 2 x 2 x 3 x 17

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 = 7140 = 2 x 2 x 3 x 5 x 7 x 17

Step 4: Therefore, the least common multiple of 204 and 210 is 7140.