Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 8577 and 8584 the smallest integer that is 73624968 that is divisible by both numbers.
Least Common Multiple (LCM) of 8577 and 8584 is 73624968.
LCM(8577,8584) = 73624968
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 8577 and 8584. First we will calculate the prime factors of 8577 and 8584.
Prime Factorization of 8577
3 | 8577 |
3 | 2859 |
953 | 953 |
1 |
Prime factors of 8577 are 3,953. Prime factorization of 8577 in exponential form is:
8577 = 32×9531
Prime Factorization of 8584
2 | 8584 |
2 | 4292 |
2 | 2146 |
29 | 1073 |
37 | 37 |
1 |
Prime factors of 8584 are 2, 29,37. Prime factorization of 8584 in exponential form is:
8584 = 23×291×371
Now multiplying the highest exponent prime factors to calculate the LCM of 8577 and 8584.
LCM(8577,8584) = 23×32×291×371×9531
LCM(8577,8584) = 73624968
Factors of 8577
List of positive integer factors of 8577 that divides 8577 without a remainder.
1, 3, 9, 953, 2859, 8577
Factors of 8584
List of positive integer factors of 8584 that divides 8584 without a remainder.
1, 2, 4, 8, 29, 37, 58, 74, 116, 148, 232, 296, 1073, 2146, 4292, 8584
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8577 and 8584, than apply into the LCM equation.
GCF(8577,8584) = 1
LCM(8577,8584) = ( 8577 × 8584) / 1
LCM(8577,8584) = 73624968 / 1
LCM(8577,8584) = 73624968
(i) The LCM of 8584 and 8577 is associative
LCM of 8577 and 8584 = LCM of 8584 and 8577
1. What is the LCM of 8577 and 8584?
Answer: LCM of 8577 and 8584 is 73624968.
2. What are the Factors of 8577?
Answer: Factors of 8577 are 1, 3, 9, 953, 2859, 8577. There are 6 integers that are factors of 8577. The greatest factor of 8577 is 8577.
3. What are the Factors of 8584?
Answer: Factors of 8584 are 1, 2, 4, 8, 29, 37, 58, 74, 116, 148, 232, 296, 1073, 2146, 4292, 8584. There are 16 integers that are factors of 8584. The greatest factor of 8584 is 8584.
4. How to Find the LCM of 8577 and 8584?
Answer:
Least Common Multiple of 8577 and 8584 = 73624968
Step 1: Find the prime factorization of 8577
8577 = 3 x 3 x 953
Step 2: Find the prime factorization of 8584
8584 = 2 x 2 x 2 x 29 x 37
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 73624968 = 2 x 2 x 2 x 3 x 3 x 29 x 37 x 953
Step 4: Therefore, the least common multiple of 8577 and 8584 is 73624968.