Least Common Multiple of 224 and 231

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 224 and 231 the smallest integer that is 7392 that is divisible by both numbers.

Least Common Multiple (LCM) of 224 and 231 is 7392.

LCM(224,231) = 7392

LCM of 224 and 231

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

LCM of:
and

Least Common Multiple of 224 and 231

LCM of 224 and 231 is 7392

Least common multiple can be found by multiplying the highest exponent prime factors of 224 and 231. First we will calculate the prime factors of 224 and 231.

Prime Factorization of 224


2 224
2 112
2 56
2 28
2 14
7 7
1

Prime factors of 224 are 2,7. Prime factorization of 224 in exponential form is:

224 = 25×71

Prime Factorization of 231


3 231
7 77
11 11
1

Prime factors of 231 are 3, 7,11. Prime factorization of 231 in exponential form is:

231 = 31×71×111

Now multiplying the highest exponent prime factors to calculate the LCM of 224 and 231.

LCM(224,231) = 25×31×71×111
LCM(224,231) = 7392

Factors of 224

List of positive integer factors of 224 that divides 224 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224

Factors of 231

List of positive integer factors of 231 that divides 231 without a remainder.

1, 3, 7, 11, 21, 33, 77, 231

Least Common Multiple of 224 and 231 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 224 and 231, than apply into the LCM equation.

GCF(224,231) = 7
LCM(224,231) = ( 224 × 231) / 7
LCM(224,231) = 51744 / 7
LCM(224,231) = 7392

Properties of LCM 224 and 231

(i) The LCM of 231 and 224 is associative

LCM of 224 and 231 = LCM of 231 and 224

Related Least Common Multiples of 224

Related Least Common Multiples of 231

Frequently Asked Questions on LCM of 224 and 231

1. What is the LCM of 224 and 231?

Answer: LCM of 224 and 231 is 7392.

2. What are the Factors of 224?

Answer: Factors of 224 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224. There are 12 integers that are factors of 224. The greatest factor of 224 is 224.

3. What are the Factors of 231?

Answer: Factors of 231 are 1, 3, 7, 11, 21, 33, 77, 231. There are 8 integers that are factors of 231. The greatest factor of 231 is 231.

4. How to Find the LCM of 224 and 231?

Answer:

Least Common Multiple of 224 and 231 = 7392

Step 1: Find the prime factorization of 224

224 = 2 x 2 x 2 x 2 x 2 x 7

Step 2: Find the prime factorization of 231

231 = 3 x 7 x 11

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

LCM = 7392 = 2 x 2 x 2 x 2 x 2 x 3 x 7 x 11

Step 4: Therefore, the least common multiple of 224 and 231 is 7392.