Least Common Multiple of 224 and 230

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 230 the smallest integer that is 25760 that is divisible by both numbers.

Least Common Multiple (LCM) of 224 and 230 is 25760.

LCM(224,230) = 25760

LCM of 224 and 230

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

LCM of:
and

Least Common Multiple of 224 and 230

LCM of 224 and 230 is 25760

Least common multiple can be found by multiplying the highest exponent prime factors of 224 and 230. First we will calculate the prime factors of 224 and 230.

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 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

Now multiplying the highest exponent prime factors to calculate the LCM of 224 and 230.

LCM(224,230) = 25×51×71×231
LCM(224,230) = 25760

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 230

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

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

Least Common Multiple of 224 and 230 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 230, than apply into the LCM equation.

GCF(224,230) = 2
LCM(224,230) = ( 224 × 230) / 2
LCM(224,230) = 51520 / 2
LCM(224,230) = 25760

Properties of LCM 224 and 230

(i) The LCM of 230 and 224 is associative

LCM of 224 and 230 = LCM of 230 and 224

Related Least Common Multiples of 224

Related Least Common Multiples of 230

Frequently Asked Questions on LCM of 224 and 230

1. What is the LCM of 224 and 230?

Answer: LCM of 224 and 230 is 25760.

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 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.

4. How to Find the LCM of 224 and 230?

Answer:

Least Common Multiple of 224 and 230 = 25760

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 230

230 = 2 x 5 x 23

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

LCM = 25760 = 2 x 2 x 2 x 2 x 2 x 5 x 7 x 23

Step 4: Therefore, the least common multiple of 224 and 230 is 25760.