Least Common Multiple of 507 and 510
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 507 and 510 the smallest integer that is 86190 that is divisible by both numbers.
Least Common Multiple (LCM) of 507 and 510 is 86190.
LCM(507,510) = 86190
LCM of 507 and 510
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 507 and 510 by Prime method
- Least Common Multiple of 507 and 510 with GCF Formula
LCM of 507 and 510 is 86190
Least common multiple can be found by multiplying the highest exponent prime factors of 507 and 510. First we will calculate the prime factors of 507 and 510.
Prime Factorization of 507
| 3 | 507 |
| 13 | 169 |
| 13 | 13 |
| 1 |
Prime factors of 507 are 3,13. Prime factorization of 507 in exponential form is:
507 = 31×132
Prime Factorization of 510
| 2 | 510 |
| 3 | 255 |
| 5 | 85 |
| 17 | 17 |
| 1 |
Prime factors of 510 are 2, 3, 5,17. Prime factorization of 510 in exponential form is:
510 = 21×31×51×171
Now multiplying the highest exponent prime factors to calculate the LCM of 507 and 510.
LCM(507,510) = 21×31×51×132×171
LCM(507,510) = 86190
Factors of 507
List of positive integer factors of 507 that divides 507 without a remainder.
1, 3, 13, 39, 169, 507
Factors of 510
List of positive integer factors of 510 that divides 510 without a remainder.
1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 102, 170, 255, 510
Least Common Multiple of 507 and 510 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 507 and 510, than apply into the LCM equation.
GCF(507,510) = 3
LCM(507,510) = ( 507 × 510) / 3
LCM(507,510) = 258570 / 3
LCM(507,510) = 86190
Properties of LCM 507 and 510
(i) The LCM of 510 and 507 is associative
LCM of 507 and 510 = LCM of 510 and 507
Related Least Common Multiples of 507
Related Least Common Multiples of 510
Frequently Asked Questions on LCM of 507 and 510
1. What is the LCM of 507 and 510?
Answer: LCM of 507 and 510 is 86190.
2. What are the Factors of 507?
Answer: Factors of 507 are 1, 3, 13, 39, 169, 507. There are 6 integers that are factors of 507. The greatest factor of 507 is 507.
3. What are the Factors of 510?
Answer: Factors of 510 are 1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 102, 170, 255, 510. There are 16 integers that are factors of 510. The greatest factor of 510 is 510.
4. How to Find the LCM of 507 and 510?
Answer:
Least Common Multiple of 507 and 510 = 86190
Step 1: Find the prime factorization of 507
507 = 3 x 13 x 13
Step 2: Find the prime factorization of 510
510 = 2 x 3 x 5 x 17
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 86190 = 2 x 3 x 5 x 13 x 13 x 17
Step 4: Therefore, the least common multiple of 507 and 510 is 86190.
