Least Common Multiple of 230 and 238

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 230 and 238 the smallest integer that is 27370 that is divisible by both numbers.

Least Common Multiple (LCM) of 230 and 238 is 27370.

LCM(230,238) = 27370

LCM of 230 and 238

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

LCM of:
and

Least Common Multiple of 230 and 238

LCM of 230 and 238 is 27370

Least common multiple can be found by multiplying the highest exponent prime factors of 230 and 238. First we will calculate the prime factors of 230 and 238.

Prime Factorization of 230


2 230
5 115
23 23
1

Prime factors of 230 are 2, 5,23. Prime factorization of 230 in exponential form is:

230 = 21×51×231

Prime Factorization of 238


2 238
7 119
17 17
1

Prime factors of 238 are 2, 7,17. Prime factorization of 238 in exponential form is:

238 = 21×71×171

Now multiplying the highest exponent prime factors to calculate the LCM of 230 and 238.

LCM(230,238) = 21×51×71×171×231
LCM(230,238) = 27370

Factors of 230

List of positive integer factors of 230 that divides 230 without a remainder.

1, 2, 5, 10, 23, 46, 115, 230

Factors of 238

List of positive integer factors of 238 that divides 238 without a remainder.

1, 2, 7, 14, 17, 34, 119, 238

Least Common Multiple of 230 and 238 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 230 and 238, than apply into the LCM equation.

GCF(230,238) = 2
LCM(230,238) = ( 230 × 238) / 2
LCM(230,238) = 54740 / 2
LCM(230,238) = 27370

Properties of LCM 230 and 238

(i) The LCM of 238 and 230 is associative

LCM of 230 and 238 = LCM of 238 and 230

Related Least Common Multiples of 230

Related Least Common Multiples of 238

Frequently Asked Questions on LCM of 230 and 238

1. What is the LCM of 230 and 238?

Answer: LCM of 230 and 238 is 27370.

2. What are the Factors of 230?

Answer: Factors of 230 are 1, 2, 5, 10, 23, 46, 115, 230. There are 8 integers that are factors of 230. The greatest factor of 230 is 230.

3. What are the Factors of 238?

Answer: Factors of 238 are 1, 2, 7, 14, 17, 34, 119, 238. There are 8 integers that are factors of 238. The greatest factor of 238 is 238.

4. How to Find the LCM of 230 and 238?

Answer:

Least Common Multiple of 230 and 238 = 27370

Step 1: Find the prime factorization of 230

230 = 2 x 5 x 23

Step 2: Find the prime factorization of 238

238 = 2 x 7 x 17

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

LCM = 27370 = 2 x 5 x 7 x 17 x 23

Step 4: Therefore, the least common multiple of 230 and 238 is 27370.