Least Common Multiple of 219 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 219 and 224 the smallest integer that is 49056 that is divisible by both numbers.

Least Common Multiple (LCM) of 219 and 224 is 49056.

LCM(219,224) = 49056

LCM of 219 and 224

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

LCM of:
and

Least Common Multiple of 219 and 224

LCM of 219 and 224 is 49056

Least common multiple can be found by multiplying the highest exponent prime factors of 219 and 224. First we will calculate the prime factors of 219 and 224.

Prime Factorization of 219


3 219
73 73
1

Prime factors of 219 are 3,73. Prime factorization of 219 in exponential form is:

219 = 31×731

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 219 and 224.

LCM(219,224) = 25×31×71×731
LCM(219,224) = 49056

Factors of 219

List of positive integer factors of 219 that divides 219 without a remainder.

1, 3, 73, 219

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 219 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 219 and 224, than apply into the LCM equation.

GCF(219,224) = 1
LCM(219,224) = ( 219 × 224) / 1
LCM(219,224) = 49056 / 1
LCM(219,224) = 49056

Properties of LCM 219 and 224

(i) The LCM of 224 and 219 is associative

LCM of 219 and 224 = LCM of 224 and 219

Related Least Common Multiples of 219

Related Least Common Multiples of 224

Frequently Asked Questions on LCM of 219 and 224

1. What is the LCM of 219 and 224?

Answer: LCM of 219 and 224 is 49056.

2. What are the Factors of 219?

Answer: Factors of 219 are 1, 3, 73, 219. There are 4 integers that are factors of 219. The greatest factor of 219 is 219.

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 219 and 224?

Answer:

Least Common Multiple of 219 and 224 = 49056

Step 1: Find the prime factorization of 219

219 = 3 x 73

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 = 49056 = 2 x 2 x 2 x 2 x 2 x 3 x 7 x 73

Step 4: Therefore, the least common multiple of 219 and 224 is 49056.