Least Common Multiple of 218 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 218 and 224 the smallest integer that is 24416 that is divisible by both numbers.

Least Common Multiple (LCM) of 218 and 224 is 24416.

LCM(218,224) = 24416

LCM of 218 and 224

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

LCM of:
and

Least Common Multiple of 218 and 224

LCM of 218 and 224 is 24416

Least common multiple can be found by multiplying the highest exponent prime factors of 218 and 224. First we will calculate the prime factors of 218 and 224.

Prime Factorization of 218


2 218
109 109
1

Prime factors of 218 are 2,109. Prime factorization of 218 in exponential form is:

218 = 21×1091

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 218 and 224.

LCM(218,224) = 25×71×1091
LCM(218,224) = 24416

Factors of 218

List of positive integer factors of 218 that divides 218 without a remainder.

1, 2, 109, 218

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 218 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 218 and 224, than apply into the LCM equation.

GCF(218,224) = 2
LCM(218,224) = ( 218 × 224) / 2
LCM(218,224) = 48832 / 2
LCM(218,224) = 24416

Properties of LCM 218 and 224

(i) The LCM of 224 and 218 is associative

LCM of 218 and 224 = LCM of 224 and 218

Related Least Common Multiples of 218

Related Least Common Multiples of 224

Frequently Asked Questions on LCM of 218 and 224

1. What is the LCM of 218 and 224?

Answer: LCM of 218 and 224 is 24416.

2. What are the Factors of 218?

Answer: Factors of 218 are 1, 2, 109, 218. There are 4 integers that are factors of 218. The greatest factor of 218 is 218.

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 218 and 224?

Answer:

Least Common Multiple of 218 and 224 = 24416

Step 1: Find the prime factorization of 218

218 = 2 x 109

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 = 24416 = 2 x 2 x 2 x 2 x 2 x 7 x 109

Step 4: Therefore, the least common multiple of 218 and 224 is 24416.