Least Common Multiple of 2232 and 2240

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 2232 and 2240 the smallest integer that is 624960 that is divisible by both numbers.

Least Common Multiple (LCM) of 2232 and 2240 is 624960.

LCM(2232,2240) = 624960

LCM of 2232 and 2240

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

LCM of:
and

Least Common Multiple of 2232 and 2240

LCM of 2232 and 2240 is 624960

Least common multiple can be found by multiplying the highest exponent prime factors of 2232 and 2240. First we will calculate the prime factors of 2232 and 2240.

Prime Factorization of 2232


2 2232
2 1116
2 558
3 279
3 93
31 31
1

Prime factors of 2232 are 2, 3,31. Prime factorization of 2232 in exponential form is:

2232 = 23×32×311

Prime Factorization of 2240


2 2240
2 1120
2 560
2 280
2 140
2 70
5 35
7 7
1

Prime factors of 2240 are 2, 5,7. Prime factorization of 2240 in exponential form is:

2240 = 26×51×71

Now multiplying the highest exponent prime factors to calculate the LCM of 2232 and 2240.

LCM(2232,2240) = 26×32×51×71×311
LCM(2232,2240) = 624960

Factors of 2232

List of positive integer factors of 2232 that divides 2232 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 31, 36, 62, 72, 93, 124, 186, 248, 279, 372, 558, 744, 1116, 2232

Factors of 2240

List of positive integer factors of 2240 that divides 2240 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 32, 35, 40, 56, 64, 70, 80, 112, 140, 160, 224, 280, 320, 448, 560, 1120, 2240

Least Common Multiple of 2232 and 2240 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2232 and 2240, than apply into the LCM equation.

GCF(2232,2240) = 8
LCM(2232,2240) = ( 2232 × 2240) / 8
LCM(2232,2240) = 4999680 / 8
LCM(2232,2240) = 624960

Properties of LCM 2232 and 2240

(i) The LCM of 2240 and 2232 is associative

LCM of 2232 and 2240 = LCM of 2240 and 2232

Related Least Common Multiples of 2232

Related Least Common Multiples of 2240

Frequently Asked Questions on LCM of 2232 and 2240

1. What is the LCM of 2232 and 2240?

Answer: LCM of 2232 and 2240 is 624960.

2. What are the Factors of 2232?

Answer: Factors of 2232 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 31, 36, 62, 72, 93, 124, 186, 248, 279, 372, 558, 744, 1116, 2232. There are 24 integers that are factors of 2232. The greatest factor of 2232 is 2232.

3. What are the Factors of 2240?

Answer: Factors of 2240 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 32, 35, 40, 56, 64, 70, 80, 112, 140, 160, 224, 280, 320, 448, 560, 1120, 2240. There are 28 integers that are factors of 2240. The greatest factor of 2240 is 2240.

4. How to Find the LCM of 2232 and 2240?

Answer:

Least Common Multiple of 2232 and 2240 = 624960

Step 1: Find the prime factorization of 2232

2232 = 2 x 2 x 2 x 3 x 3 x 31

Step 2: Find the prime factorization of 2240

2240 = 2 x 2 x 2 x 2 x 2 x 2 x 5 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 = 624960 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5 x 7 x 31

Step 4: Therefore, the least common multiple of 2232 and 2240 is 624960.