Least Common Multiple of 222 and 224

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 222 and 224 the smallest integer that is 24864 that is divisible by both numbers.

Least Common Multiple (LCM) of 222 and 224 is 24864.

LCM(222,224) = 24864

LCM of 222 and 224

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

LCM of:
and

Least Common Multiple of 222 and 224

LCM of 222 and 224 is 24864

Least common multiple can be found by multiplying the highest exponent prime factors of 222 and 224. First we will calculate the prime factors of 222 and 224.

Prime Factorization of 222


2 222
3 111
37 37
1

Prime factors of 222 are 2, 3,37. Prime factorization of 222 in exponential form is:

222 = 21×31×371

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

Now multiplying the highest exponent prime factors to calculate the LCM of 222 and 224.

LCM(222,224) = 25×31×71×371
LCM(222,224) = 24864

Factors of 222

List of positive integer factors of 222 that divides 222 without a remainder.

1, 2, 3, 6, 37, 74, 111, 222

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

Least Common Multiple of 222 and 224 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 222 and 224, than apply into the LCM equation.

GCF(222,224) = 2
LCM(222,224) = ( 222 × 224) / 2
LCM(222,224) = 49728 / 2
LCM(222,224) = 24864

Properties of LCM 222 and 224

(i) The LCM of 224 and 222 is associative

LCM of 222 and 224 = LCM of 224 and 222

Related Least Common Multiples of 222

Related Least Common Multiples of 224

Frequently Asked Questions on LCM of 222 and 224

1. What is the LCM of 222 and 224?

Answer: LCM of 222 and 224 is 24864.

2. What are the Factors of 222?

Answer: Factors of 222 are 1, 2, 3, 6, 37, 74, 111, 222. There are 8 integers that are factors of 222. The greatest factor of 222 is 222.

3. 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.

4. How to Find the LCM of 222 and 224?

Answer:

Least Common Multiple of 222 and 224 = 24864

Step 1: Find the prime factorization of 222

222 = 2 x 3 x 37

Step 2: Find the prime factorization of 224

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

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

LCM = 24864 = 2 x 2 x 2 x 2 x 2 x 3 x 7 x 37

Step 4: Therefore, the least common multiple of 222 and 224 is 24864.