Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 2578 and 2584 the smallest integer that is 3330776 that is divisible by both numbers.
Least Common Multiple (LCM) of 2578 and 2584 is 3330776.
LCM(2578,2584) = 3330776
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 2578 and 2584. First we will calculate the prime factors of 2578 and 2584.
Prime Factorization of 2578
2 | 2578 |
1289 | 1289 |
1 |
Prime factors of 2578 are 2,1289. Prime factorization of 2578 in exponential form is:
2578 = 21×12891
Prime Factorization of 2584
2 | 2584 |
2 | 1292 |
2 | 646 |
17 | 323 |
19 | 19 |
1 |
Prime factors of 2584 are 2, 17,19. Prime factorization of 2584 in exponential form is:
2584 = 23×171×191
Now multiplying the highest exponent prime factors to calculate the LCM of 2578 and 2584.
LCM(2578,2584) = 23×171×191×12891
LCM(2578,2584) = 3330776
Factors of 2578
List of positive integer factors of 2578 that divides 2578 without a remainder.
1, 2, 1289, 2578
Factors of 2584
List of positive integer factors of 2584 that divides 2584 without a remainder.
1, 2, 4, 8, 17, 19, 34, 38, 68, 76, 136, 152, 323, 646, 1292, 2584
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2578 and 2584, than apply into the LCM equation.
GCF(2578,2584) = 2
LCM(2578,2584) = ( 2578 × 2584) / 2
LCM(2578,2584) = 6661552 / 2
LCM(2578,2584) = 3330776
(i) The LCM of 2584 and 2578 is associative
LCM of 2578 and 2584 = LCM of 2584 and 2578
1. What is the LCM of 2578 and 2584?
Answer: LCM of 2578 and 2584 is 3330776.
2. What are the Factors of 2578?
Answer: Factors of 2578 are 1, 2, 1289, 2578. There are 4 integers that are factors of 2578. The greatest factor of 2578 is 2578.
3. What are the Factors of 2584?
Answer: Factors of 2584 are 1, 2, 4, 8, 17, 19, 34, 38, 68, 76, 136, 152, 323, 646, 1292, 2584. There are 16 integers that are factors of 2584. The greatest factor of 2584 is 2584.
4. How to Find the LCM of 2578 and 2584?
Answer:
Least Common Multiple of 2578 and 2584 = 3330776
Step 1: Find the prime factorization of 2578
2578 = 2 x 1289
Step 2: Find the prime factorization of 2584
2584 = 2 x 2 x 2 x 17 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 = 3330776 = 2 x 2 x 2 x 17 x 19 x 1289
Step 4: Therefore, the least common multiple of 2578 and 2584 is 3330776.