Least Common Multiple of 216 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 216 and 224 the smallest integer that is 6048 that is divisible by both numbers.

Least Common Multiple (LCM) of 216 and 224 is 6048.

LCM(216,224) = 6048

LCM of 216 and 224

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

LCM of:
and

Least Common Multiple of 216 and 224

LCM of 216 and 224 is 6048

Least common multiple can be found by multiplying the highest exponent prime factors of 216 and 224. First we will calculate the prime factors of 216 and 224.

Prime Factorization of 216


2 216
2 108
2 54
3 27
3 9
3 3
1

Prime factors of 216 are 2,3. Prime factorization of 216 in exponential form is:

216 = 23×33

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 216 and 224.

LCM(216,224) = 25×33×71
LCM(216,224) = 6048

Factors of 216

List of positive integer factors of 216 that divides 216 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216

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 216 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 216 and 224, than apply into the LCM equation.

GCF(216,224) = 8
LCM(216,224) = ( 216 × 224) / 8
LCM(216,224) = 48384 / 8
LCM(216,224) = 6048

Properties of LCM 216 and 224

(i) The LCM of 224 and 216 is associative

LCM of 216 and 224 = LCM of 224 and 216

Related Least Common Multiples of 216

Related Least Common Multiples of 224

Frequently Asked Questions on LCM of 216 and 224

1. What is the LCM of 216 and 224?

Answer: LCM of 216 and 224 is 6048.

2. What are the Factors of 216?

Answer: Factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216. There are 16 integers that are factors of 216. The greatest factor of 216 is 216.

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 216 and 224?

Answer:

Least Common Multiple of 216 and 224 = 6048

Step 1: Find the prime factorization of 216

216 = 2 x 2 x 2 x 3 x 3 x 3

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 = 6048 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 7

Step 4: Therefore, the least common multiple of 216 and 224 is 6048.