Least Common Multiple of 224 and 232

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 232 the smallest integer that is 6496 that is divisible by both numbers.

Least Common Multiple (LCM) of 224 and 232 is 6496.

LCM(224,232) = 6496

LCM of 224 and 232

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

LCM of:
and

Least Common Multiple of 224 and 232

LCM of 224 and 232 is 6496

Least common multiple can be found by multiplying the highest exponent prime factors of 224 and 232. First we will calculate the prime factors of 224 and 232.

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 232


2 232
2 116
2 58
29 29
1

Prime factors of 232 are 2,29. Prime factorization of 232 in exponential form is:

232 = 23×291

Now multiplying the highest exponent prime factors to calculate the LCM of 224 and 232.

LCM(224,232) = 25×71×291
LCM(224,232) = 6496

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 232

List of positive integer factors of 232 that divides 232 without a remainder.

1, 2, 4, 8, 29, 58, 116, 232

Least Common Multiple of 224 and 232 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 232, than apply into the LCM equation.

GCF(224,232) = 8
LCM(224,232) = ( 224 × 232) / 8
LCM(224,232) = 51968 / 8
LCM(224,232) = 6496

Properties of LCM 224 and 232

(i) The LCM of 232 and 224 is associative

LCM of 224 and 232 = LCM of 232 and 224

Related Least Common Multiples of 224

Related Least Common Multiples of 232

Frequently Asked Questions on LCM of 224 and 232

1. What is the LCM of 224 and 232?

Answer: LCM of 224 and 232 is 6496.

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 232?

Answer: Factors of 232 are 1, 2, 4, 8, 29, 58, 116, 232. There are 8 integers that are factors of 232. The greatest factor of 232 is 232.

4. How to Find the LCM of 224 and 232?

Answer:

Least Common Multiple of 224 and 232 = 6496

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 232

232 = 2 x 2 x 2 x 29

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

LCM = 6496 = 2 x 2 x 2 x 2 x 2 x 7 x 29

Step 4: Therefore, the least common multiple of 224 and 232 is 6496.