Least Common Multiple of 2280 and 2288

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 2280 and 2288 the smallest integer that is 652080 that is divisible by both numbers.

Least Common Multiple (LCM) of 2280 and 2288 is 652080.

LCM(2280,2288) = 652080

LCM of 2280 and 2288

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

LCM of:
and

Least Common Multiple of 2280 and 2288

LCM of 2280 and 2288 is 652080

Least common multiple can be found by multiplying the highest exponent prime factors of 2280 and 2288. First we will calculate the prime factors of 2280 and 2288.

Prime Factorization of 2280


2 2280
2 1140
2 570
3 285
5 95
19 19
1

Prime factors of 2280 are 2, 3, 5,19. Prime factorization of 2280 in exponential form is:

2280 = 23×31×51×191

Prime Factorization of 2288


2 2288
2 1144
2 572
2 286
11 143
13 13
1

Prime factors of 2288 are 2, 11,13. Prime factorization of 2288 in exponential form is:

2288 = 24×111×131

Now multiplying the highest exponent prime factors to calculate the LCM of 2280 and 2288.

LCM(2280,2288) = 24×31×51×111×131×191
LCM(2280,2288) = 652080

Factors of 2280

List of positive integer factors of 2280 that divides 2280 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 19, 20, 24, 30, 38, 40, 57, 60, 76, 95, 114, 120, 152, 190, 228, 285, 380, 456, 570, 760, 1140, 2280

Factors of 2288

List of positive integer factors of 2288 that divides 2288 without a remainder.

1, 2, 4, 8, 11, 13, 16, 22, 26, 44, 52, 88, 104, 143, 176, 208, 286, 572, 1144, 2288

Least Common Multiple of 2280 and 2288 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2280 and 2288, than apply into the LCM equation.

GCF(2280,2288) = 8
LCM(2280,2288) = ( 2280 × 2288) / 8
LCM(2280,2288) = 5216640 / 8
LCM(2280,2288) = 652080

Properties of LCM 2280 and 2288

(i) The LCM of 2288 and 2280 is associative

LCM of 2280 and 2288 = LCM of 2288 and 2280

Related Least Common Multiples of 2280

Related Least Common Multiples of 2288

Frequently Asked Questions on LCM of 2280 and 2288

1. What is the LCM of 2280 and 2288?

Answer: LCM of 2280 and 2288 is 652080.

2. What are the Factors of 2280?

Answer: Factors of 2280 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 19, 20, 24, 30, 38, 40, 57, 60, 76, 95, 114, 120, 152, 190, 228, 285, 380, 456, 570, 760, 1140, 2280. There are 32 integers that are factors of 2280. The greatest factor of 2280 is 2280.

3. What are the Factors of 2288?

Answer: Factors of 2288 are 1, 2, 4, 8, 11, 13, 16, 22, 26, 44, 52, 88, 104, 143, 176, 208, 286, 572, 1144, 2288. There are 20 integers that are factors of 2288. The greatest factor of 2288 is 2288.

4. How to Find the LCM of 2280 and 2288?

Answer:

Least Common Multiple of 2280 and 2288 = 652080

Step 1: Find the prime factorization of 2280

2280 = 2 x 2 x 2 x 3 x 5 x 19

Step 2: Find the prime factorization of 2288

2288 = 2 x 2 x 2 x 2 x 11 x 13

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 652080 = 2 x 2 x 2 x 2 x 3 x 5 x 11 x 13 x 19

Step 4: Therefore, the least common multiple of 2280 and 2288 is 652080.