Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 8717 and 8724 the smallest integer that is 76047108 that is divisible by both numbers.
Least Common Multiple (LCM) of 8717 and 8724 is 76047108.
LCM(8717,8724) = 76047108
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 8717 and 8724. First we will calculate the prime factors of 8717 and 8724.
Prime Factorization of 8717
23 | 8717 |
379 | 379 |
1 |
Prime factors of 8717 are 23,379. Prime factorization of 8717 in exponential form is:
8717 = 231×3791
Prime Factorization of 8724
2 | 8724 |
2 | 4362 |
3 | 2181 |
727 | 727 |
1 |
Prime factors of 8724 are 2, 3,727. Prime factorization of 8724 in exponential form is:
8724 = 22×31×7271
Now multiplying the highest exponent prime factors to calculate the LCM of 8717 and 8724.
LCM(8717,8724) = 22×31×231×3791×7271
LCM(8717,8724) = 76047108
Factors of 8717
List of positive integer factors of 8717 that divides 8717 without a remainder.
1, 23, 379, 8717
Factors of 8724
List of positive integer factors of 8724 that divides 8724 without a remainder.
1, 2, 3, 4, 6, 12, 727, 1454, 2181, 2908, 4362, 8724
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8717 and 8724, than apply into the LCM equation.
GCF(8717,8724) = 1
LCM(8717,8724) = ( 8717 × 8724) / 1
LCM(8717,8724) = 76047108 / 1
LCM(8717,8724) = 76047108
(i) The LCM of 8724 and 8717 is associative
LCM of 8717 and 8724 = LCM of 8724 and 8717
1. What is the LCM of 8717 and 8724?
Answer: LCM of 8717 and 8724 is 76047108.
2. What are the Factors of 8717?
Answer: Factors of 8717 are 1, 23, 379, 8717. There are 4 integers that are factors of 8717. The greatest factor of 8717 is 8717.
3. What are the Factors of 8724?
Answer: Factors of 8724 are 1, 2, 3, 4, 6, 12, 727, 1454, 2181, 2908, 4362, 8724. There are 12 integers that are factors of 8724. The greatest factor of 8724 is 8724.
4. How to Find the LCM of 8717 and 8724?
Answer:
Least Common Multiple of 8717 and 8724 = 76047108
Step 1: Find the prime factorization of 8717
8717 = 23 x 379
Step 2: Find the prime factorization of 8724
8724 = 2 x 2 x 3 x 727
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 76047108 = 2 x 2 x 3 x 23 x 379 x 727
Step 4: Therefore, the least common multiple of 8717 and 8724 is 76047108.