Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 2275 and 2280 the smallest integer that is 1037400 that is divisible by both numbers.
Least Common Multiple (LCM) of 2275 and 2280 is 1037400.
LCM(2275,2280) = 1037400
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
Least common multiple can be found by multiplying the highest exponent prime factors of 2275 and 2280. First we will calculate the prime factors of 2275 and 2280.
Prime Factorization of 2275
5 | 2275 |
5 | 455 |
7 | 91 |
13 | 13 |
1 |
Prime factors of 2275 are 5, 7,13. Prime factorization of 2275 in exponential form is:
2275 = 52×71×131
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
Now multiplying the highest exponent prime factors to calculate the LCM of 2275 and 2280.
LCM(2275,2280) = 23×31×52×71×131×191
LCM(2275,2280) = 1037400
Factors of 2275
List of positive integer factors of 2275 that divides 2275 without a remainder.
1, 5, 7, 13, 25, 35, 65, 91, 175, 325, 455, 2275
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
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2275 and 2280, than apply into the LCM equation.
GCF(2275,2280) = 5
LCM(2275,2280) = ( 2275 × 2280) / 5
LCM(2275,2280) = 5187000 / 5
LCM(2275,2280) = 1037400
(i) The LCM of 2280 and 2275 is associative
LCM of 2275 and 2280 = LCM of 2280 and 2275
1. What is the LCM of 2275 and 2280?
Answer: LCM of 2275 and 2280 is 1037400.
2. What are the Factors of 2275?
Answer: Factors of 2275 are 1, 5, 7, 13, 25, 35, 65, 91, 175, 325, 455, 2275. There are 12 integers that are factors of 2275. The greatest factor of 2275 is 2275.
3. 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.
4. How to Find the LCM of 2275 and 2280?
Answer:
Least Common Multiple of 2275 and 2280 = 1037400
Step 1: Find the prime factorization of 2275
2275 = 5 x 5 x 7 x 13
Step 2: Find the prime factorization of 2280
2280 = 2 x 2 x 2 x 3 x 5 x 19
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 1037400 = 2 x 2 x 2 x 3 x 5 x 5 x 7 x 13 x 19
Step 4: Therefore, the least common multiple of 2275 and 2280 is 1037400.