Least Common Multiple of 221 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 221 and 224 the smallest integer that is 49504 that is divisible by both numbers.

Least Common Multiple (LCM) of 221 and 224 is 49504.

LCM(221,224) = 49504

LCM of 221 and 224

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

LCM of:
and

Least Common Multiple of 221 and 224

LCM of 221 and 224 is 49504

Least common multiple can be found by multiplying the highest exponent prime factors of 221 and 224. First we will calculate the prime factors of 221 and 224.

Prime Factorization of 221


13 221
17 17
1

Prime factors of 221 are 13,17. Prime factorization of 221 in exponential form is:

221 = 131×171

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 221 and 224.

LCM(221,224) = 25×71×131×171
LCM(221,224) = 49504

Factors of 221

List of positive integer factors of 221 that divides 221 without a remainder.

1, 13, 17, 221

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 221 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 221 and 224, than apply into the LCM equation.

GCF(221,224) = 1
LCM(221,224) = ( 221 × 224) / 1
LCM(221,224) = 49504 / 1
LCM(221,224) = 49504

Properties of LCM 221 and 224

(i) The LCM of 224 and 221 is associative

LCM of 221 and 224 = LCM of 224 and 221

Related Least Common Multiples of 221

Related Least Common Multiples of 224

Frequently Asked Questions on LCM of 221 and 224

1. What is the LCM of 221 and 224?

Answer: LCM of 221 and 224 is 49504.

2. What are the Factors of 221?

Answer: Factors of 221 are 1, 13, 17, 221. There are 4 integers that are factors of 221. The greatest factor of 221 is 221.

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 221 and 224?

Answer:

Least Common Multiple of 221 and 224 = 49504

Step 1: Find the prime factorization of 221

221 = 13 x 17

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 = 49504 = 2 x 2 x 2 x 2 x 2 x 7 x 13 x 17

Step 4: Therefore, the least common multiple of 221 and 224 is 49504.