Least Common Multiple of 234 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 234 and 238 the smallest integer that is 27846 that is divisible by both numbers.

Least Common Multiple (LCM) of 234 and 238 is 27846.

LCM(234,238) = 27846

LCM of 234 and 238

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

LCM of:
and

Least Common Multiple of 234 and 238

LCM of 234 and 238 is 27846

Least common multiple can be found by multiplying the highest exponent prime factors of 234 and 238. First we will calculate the prime factors of 234 and 238.

Prime Factorization of 234


2 234
3 117
3 39
13 13
1

Prime factors of 234 are 2, 3,13. Prime factorization of 234 in exponential form is:

234 = 21×32×131

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 234 and 238.

LCM(234,238) = 21×32×71×131×171
LCM(234,238) = 27846

Factors of 234

List of positive integer factors of 234 that divides 234 without a remainder.

1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, 234

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 234 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 234 and 238, than apply into the LCM equation.

GCF(234,238) = 2
LCM(234,238) = ( 234 × 238) / 2
LCM(234,238) = 55692 / 2
LCM(234,238) = 27846

Properties of LCM 234 and 238

(i) The LCM of 238 and 234 is associative

LCM of 234 and 238 = LCM of 238 and 234

Related Least Common Multiples of 234

Related Least Common Multiples of 238

Frequently Asked Questions on LCM of 234 and 238

1. What is the LCM of 234 and 238?

Answer: LCM of 234 and 238 is 27846.

2. What are the Factors of 234?

Answer: Factors of 234 are 1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, 234. There are 12 integers that are factors of 234. The greatest factor of 234 is 234.

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 234 and 238?

Answer:

Least Common Multiple of 234 and 238 = 27846

Step 1: Find the prime factorization of 234

234 = 2 x 3 x 3 x 13

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 = 27846 = 2 x 3 x 3 x 7 x 13 x 17

Step 4: Therefore, the least common multiple of 234 and 238 is 27846.