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 2283 the smallest integer that is 1735080 that is divisible by both numbers.
Least Common Multiple (LCM) of 2280 and 2283 is 1735080.
LCM(2280,2283) = 1735080
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 2280 and 2283. First we will calculate the prime factors of 2280 and 2283.
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 2283
3 | 2283 |
761 | 761 |
1 |
Prime factors of 2283 are 3,761. Prime factorization of 2283 in exponential form is:
2283 = 31×7611
Now multiplying the highest exponent prime factors to calculate the LCM of 2280 and 2283.
LCM(2280,2283) = 23×31×51×191×7611
LCM(2280,2283) = 1735080
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 2283
List of positive integer factors of 2283 that divides 2283 without a remainder.
1, 3, 761, 2283
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2280 and 2283, than apply into the LCM equation.
GCF(2280,2283) = 3
LCM(2280,2283) = ( 2280 × 2283) / 3
LCM(2280,2283) = 5205240 / 3
LCM(2280,2283) = 1735080
(i) The LCM of 2283 and 2280 is associative
LCM of 2280 and 2283 = LCM of 2283 and 2280
1. What is the LCM of 2280 and 2283?
Answer: LCM of 2280 and 2283 is 1735080.
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 2283?
Answer: Factors of 2283 are 1, 3, 761, 2283. There are 4 integers that are factors of 2283. The greatest factor of 2283 is 2283.
4. How to Find the LCM of 2280 and 2283?
Answer:
Least Common Multiple of 2280 and 2283 = 1735080
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 2283
2283 = 3 x 761
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 1735080 = 2 x 2 x 2 x 3 x 5 x 19 x 761
Step 4: Therefore, the least common multiple of 2280 and 2283 is 1735080.