Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 517 and 522 the smallest integer that is 269874 that is divisible by both numbers.
Least Common Multiple (LCM) of 517 and 522 is 269874.
LCM(517,522) = 269874
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 517 and 522. First we will calculate the prime factors of 517 and 522.
Prime Factorization of 517
11 | 517 |
47 | 47 |
1 |
Prime factors of 517 are 11,47. Prime factorization of 517 in exponential form is:
517 = 111×471
Prime Factorization of 522
2 | 522 |
3 | 261 |
3 | 87 |
29 | 29 |
1 |
Prime factors of 522 are 2, 3,29. Prime factorization of 522 in exponential form is:
522 = 21×32×291
Now multiplying the highest exponent prime factors to calculate the LCM of 517 and 522.
LCM(517,522) = 21×32×111×291×471
LCM(517,522) = 269874
Factors of 517
List of positive integer factors of 517 that divides 517 without a remainder.
1, 11, 47, 517
Factors of 522
List of positive integer factors of 522 that divides 522 without a remainder.
1, 2, 3, 6, 9, 18, 29, 58, 87, 174, 261, 522
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 517 and 522, than apply into the LCM equation.
GCF(517,522) = 1
LCM(517,522) = ( 517 × 522) / 1
LCM(517,522) = 269874 / 1
LCM(517,522) = 269874
(i) The LCM of 522 and 517 is associative
LCM of 517 and 522 = LCM of 522 and 517
1. What is the LCM of 517 and 522?
Answer: LCM of 517 and 522 is 269874.
2. What are the Factors of 517?
Answer: Factors of 517 are 1, 11, 47, 517. There are 4 integers that are factors of 517. The greatest factor of 517 is 517.
3. What are the Factors of 522?
Answer: Factors of 522 are 1, 2, 3, 6, 9, 18, 29, 58, 87, 174, 261, 522. There are 12 integers that are factors of 522. The greatest factor of 522 is 522.
4. How to Find the LCM of 517 and 522?
Answer:
Least Common Multiple of 517 and 522 = 269874
Step 1: Find the prime factorization of 517
517 = 11 x 47
Step 2: Find the prime factorization of 522
522 = 2 x 3 x 3 x 29
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 269874 = 2 x 3 x 3 x 11 x 29 x 47
Step 4: Therefore, the least common multiple of 517 and 522 is 269874.