Least Common Multiple of 210 and 225

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 210 and 225 the smallest integer that is 3150 that is divisible by both numbers.

Least Common Multiple (LCM) of 210 and 225 is 3150.

LCM(210,225) = 3150

LCM of 210 and 225

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

LCM of:
and

Least Common Multiple of 210 and 225

LCM of 210 and 225 is 3150

Least common multiple can be found by multiplying the highest exponent prime factors of 210 and 225. First we will calculate the prime factors of 210 and 225.

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

Prime Factorization of 225


3 225
3 75
5 25
5 5
1

Prime factors of 225 are 3,5. Prime factorization of 225 in exponential form is:

225 = 32×52

Now multiplying the highest exponent prime factors to calculate the LCM of 210 and 225.

LCM(210,225) = 21×32×52×71
LCM(210,225) = 3150

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

Factors of 225

List of positive integer factors of 225 that divides 225 without a remainder.

1, 3, 5, 9, 15, 25, 45, 75, 225

Least Common Multiple of 210 and 225 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 210 and 225, than apply into the LCM equation.

GCF(210,225) = 15
LCM(210,225) = ( 210 × 225) / 15
LCM(210,225) = 47250 / 15
LCM(210,225) = 3150

Properties of LCM 210 and 225

(i) The LCM of 225 and 210 is associative

LCM of 210 and 225 = LCM of 225 and 210

Related Least Common Multiples of 210

Related Least Common Multiples of 225

Frequently Asked Questions on LCM of 210 and 225

1. What is the LCM of 210 and 225?

Answer: LCM of 210 and 225 is 3150.

2. 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.

3. What are the Factors of 225?

Answer: Factors of 225 are 1, 3, 5, 9, 15, 25, 45, 75, 225. There are 9 integers that are factors of 225. The greatest factor of 225 is 225.

4. How to Find the LCM of 210 and 225?

Answer:

Least Common Multiple of 210 and 225 = 3150

Step 1: Find the prime factorization of 210

210 = 2 x 3 x 5 x 7

Step 2: Find the prime factorization of 225

225 = 3 x 3 x 5 x 5

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

LCM = 3150 = 2 x 3 x 3 x 5 x 5 x 7

Step 4: Therefore, the least common multiple of 210 and 225 is 3150.