Least Common Multiple of 224 and 228

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 228 the smallest integer that is 12768 that is divisible by both numbers.

Least Common Multiple (LCM) of 224 and 228 is 12768.

LCM(224,228) = 12768

LCM of 224 and 228

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

LCM of:
and

Least Common Multiple of 224 and 228

LCM of 224 and 228 is 12768

Least common multiple can be found by multiplying the highest exponent prime factors of 224 and 228. First we will calculate the prime factors of 224 and 228.

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 228


2 228
2 114
3 57
19 19
1

Prime factors of 228 are 2, 3,19. Prime factorization of 228 in exponential form is:

228 = 22×31×191

Now multiplying the highest exponent prime factors to calculate the LCM of 224 and 228.

LCM(224,228) = 25×31×71×191
LCM(224,228) = 12768

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 228

List of positive integer factors of 228 that divides 228 without a remainder.

1, 2, 3, 4, 6, 12, 19, 38, 57, 76, 114, 228

Least Common Multiple of 224 and 228 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 228, than apply into the LCM equation.

GCF(224,228) = 4
LCM(224,228) = ( 224 × 228) / 4
LCM(224,228) = 51072 / 4
LCM(224,228) = 12768

Properties of LCM 224 and 228

(i) The LCM of 228 and 224 is associative

LCM of 224 and 228 = LCM of 228 and 224

Related Least Common Multiples of 224

Related Least Common Multiples of 228

Frequently Asked Questions on LCM of 224 and 228

1. What is the LCM of 224 and 228?

Answer: LCM of 224 and 228 is 12768.

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 228?

Answer: Factors of 228 are 1, 2, 3, 4, 6, 12, 19, 38, 57, 76, 114, 228. There are 12 integers that are factors of 228. The greatest factor of 228 is 228.

4. How to Find the LCM of 224 and 228?

Answer:

Least Common Multiple of 224 and 228 = 12768

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 228

228 = 2 x 2 x 3 x 19

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

LCM = 12768 = 2 x 2 x 2 x 2 x 2 x 3 x 7 x 19

Step 4: Therefore, the least common multiple of 224 and 228 is 12768.