Least Common Multiple of 509 and 513

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 509 and 513 the smallest integer that is 261117 that is divisible by both numbers.

Least Common Multiple (LCM) of 509 and 513 is 261117.

LCM(509,513) = 261117

LCM of 509 and 513

Least common multiple or lowest common denominator (LCD) can be calculated in three ways;

LCM of:
and

Least Common Multiple of 509 and 513

LCM of 509 and 513 is 261117

Least common multiple can be found by multiplying the highest exponent prime factors of 509 and 513. First we will calculate the prime factors of 509 and 513.

Prime Factorization of 509


509 509
1

Prime factors of 509 are 509. Prime factorization of 509 in exponential form is:

509 = 5091

Prime Factorization of 513


3 513
3 171
3 57
19 19
1

Prime factors of 513 are 3,19. Prime factorization of 513 in exponential form is:

513 = 33×191

Now multiplying the highest exponent prime factors to calculate the LCM of 509 and 513.

LCM(509,513) = 33×191×5091
LCM(509,513) = 261117

Factors of 509

List of positive integer factors of 509 that divides 509 without a remainder.

1, 509

Factors of 513

List of positive integer factors of 513 that divides 513 without a remainder.

1, 3, 9, 19, 27, 57, 171, 513

Least Common Multiple of 509 and 513 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 509 and 513, than apply into the LCM equation.

GCF(509,513) = 1
LCM(509,513) = ( 509 × 513) / 1
LCM(509,513) = 261117 / 1
LCM(509,513) = 261117

Properties of LCM 509 and 513

(i) The LCM of 513 and 509 is associative

LCM of 509 and 513 = LCM of 513 and 509

Related Least Common Multiples of 509

Related Least Common Multiples of 513

Frequently Asked Questions on LCM of 509 and 513

1. What is the LCM of 509 and 513?

Answer: LCM of 509 and 513 is 261117.

2. What are the Factors of 509?

Answer: Factors of 509 are 1, 509. There are 2 integers that are factors of 509. The greatest factor of 509 is 509.

3. What are the Factors of 513?

Answer: Factors of 513 are 1, 3, 9, 19, 27, 57, 171, 513. There are 8 integers that are factors of 513. The greatest factor of 513 is 513.

4. How to Find the LCM of 509 and 513?

Answer:

Least Common Multiple of 509 and 513 = 261117

Step 1: Find the prime factorization of 509

509 = 509

Step 2: Find the prime factorization of 513

513 = 3 x 3 x 3 x 19

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 261117 = 3 x 3 x 3 x 19 x 509

Step 4: Therefore, the least common multiple of 509 and 513 is 261117.