Least Common Multiple of 220 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 220 and 224 the smallest integer that is 12320 that is divisible by both numbers.

Least Common Multiple (LCM) of 220 and 224 is 12320.

LCM(220,224) = 12320

LCM of 220 and 224

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

LCM of:
and

Least Common Multiple of 220 and 224

LCM of 220 and 224 is 12320

Least common multiple can be found by multiplying the highest exponent prime factors of 220 and 224. First we will calculate the prime factors of 220 and 224.

Prime Factorization of 220


2 220
2 110
5 55
11 11
1

Prime factors of 220 are 2, 5,11. Prime factorization of 220 in exponential form is:

220 = 22×51×111

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 220 and 224.

LCM(220,224) = 25×51×71×111
LCM(220,224) = 12320

Factors of 220

List of positive integer factors of 220 that divides 220 without a remainder.

1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, 220

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 220 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 220 and 224, than apply into the LCM equation.

GCF(220,224) = 4
LCM(220,224) = ( 220 × 224) / 4
LCM(220,224) = 49280 / 4
LCM(220,224) = 12320

Properties of LCM 220 and 224

(i) The LCM of 224 and 220 is associative

LCM of 220 and 224 = LCM of 224 and 220

Related Least Common Multiples of 220

Related Least Common Multiples of 224

Frequently Asked Questions on LCM of 220 and 224

1. What is the LCM of 220 and 224?

Answer: LCM of 220 and 224 is 12320.

2. What are the Factors of 220?

Answer: Factors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, 220. There are 12 integers that are factors of 220. The greatest factor of 220 is 220.

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 220 and 224?

Answer:

Least Common Multiple of 220 and 224 = 12320

Step 1: Find the prime factorization of 220

220 = 2 x 2 x 5 x 11

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 = 12320 = 2 x 2 x 2 x 2 x 2 x 5 x 7 x 11

Step 4: Therefore, the least common multiple of 220 and 224 is 12320.