Least Common Multiple of 217 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 217 and 224 the smallest integer that is 6944 that is divisible by both numbers.

Least Common Multiple (LCM) of 217 and 224 is 6944.

LCM(217,224) = 6944

LCM of 217 and 224

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

LCM of:
and

Least Common Multiple of 217 and 224

LCM of 217 and 224 is 6944

Least common multiple can be found by multiplying the highest exponent prime factors of 217 and 224. First we will calculate the prime factors of 217 and 224.

Prime Factorization of 217


7 217
31 31
1

Prime factors of 217 are 7,31. Prime factorization of 217 in exponential form is:

217 = 71×311

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 217 and 224.

LCM(217,224) = 25×71×311
LCM(217,224) = 6944

Factors of 217

List of positive integer factors of 217 that divides 217 without a remainder.

1, 7, 31, 217

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 217 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 217 and 224, than apply into the LCM equation.

GCF(217,224) = 7
LCM(217,224) = ( 217 × 224) / 7
LCM(217,224) = 48608 / 7
LCM(217,224) = 6944

Properties of LCM 217 and 224

(i) The LCM of 224 and 217 is associative

LCM of 217 and 224 = LCM of 224 and 217

Related Least Common Multiples of 217

Related Least Common Multiples of 224

Frequently Asked Questions on LCM of 217 and 224

1. What is the LCM of 217 and 224?

Answer: LCM of 217 and 224 is 6944.

2. What are the Factors of 217?

Answer: Factors of 217 are 1, 7, 31, 217. There are 4 integers that are factors of 217. The greatest factor of 217 is 217.

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 217 and 224?

Answer:

Least Common Multiple of 217 and 224 = 6944

Step 1: Find the prime factorization of 217

217 = 7 x 31

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 = 6944 = 2 x 2 x 2 x 2 x 2 x 7 x 31

Step 4: Therefore, the least common multiple of 217 and 224 is 6944.