Least Common Multiple of 507 and 514
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 514 the smallest integer that is 260598 that is divisible by both numbers.
Least Common Multiple (LCM) of 507 and 514 is 260598.
LCM(507,514) = 260598
LCM of 507 and 514
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 507 and 514 by Prime method
- Least Common Multiple of 507 and 514 with GCF Formula
LCM of 507 and 514 is 260598
Least common multiple can be found by multiplying the highest exponent prime factors of 507 and 514. First we will calculate the prime factors of 507 and 514.
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 514
| 2 | 514 |
| 257 | 257 |
| 1 |
Prime factors of 514 are 2,257. Prime factorization of 514 in exponential form is:
514 = 21×2571
Now multiplying the highest exponent prime factors to calculate the LCM of 507 and 514.
LCM(507,514) = 21×31×132×2571
LCM(507,514) = 260598
Factors of 507
List of positive integer factors of 507 that divides 507 without a remainder.
1, 3, 13, 39, 169, 507
Factors of 514
List of positive integer factors of 514 that divides 514 without a remainder.
1, 2, 257, 514
Least Common Multiple of 507 and 514 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 514, than apply into the LCM equation.
GCF(507,514) = 1
LCM(507,514) = ( 507 × 514) / 1
LCM(507,514) = 260598 / 1
LCM(507,514) = 260598
Properties of LCM 507 and 514
(i) The LCM of 514 and 507 is associative
LCM of 507 and 514 = LCM of 514 and 507
Related Least Common Multiples of 507
Related Least Common Multiples of 514
Frequently Asked Questions on LCM of 507 and 514
1. What is the LCM of 507 and 514?
Answer: LCM of 507 and 514 is 260598.
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 514?
Answer: Factors of 514 are 1, 2, 257, 514. There are 4 integers that are factors of 514. The greatest factor of 514 is 514.
4. How to Find the LCM of 507 and 514?
Answer:
Least Common Multiple of 507 and 514 = 260598
Step 1: Find the prime factorization of 507
507 = 3 x 13 x 13
Step 2: Find the prime factorization of 514
514 = 2 x 257
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 260598 = 2 x 3 x 13 x 13 x 257
Step 4: Therefore, the least common multiple of 507 and 514 is 260598.