Least Common Multiple of 509 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 509 and 510 the smallest integer that is 259590 that is divisible by both numbers.

Least Common Multiple (LCM) of 509 and 510 is 259590.

LCM(509,510) = 259590

LCM of 509 and 510

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

LCM of:
and

Least Common Multiple of 509 and 510

LCM of 509 and 510 is 259590

Least common multiple can be found by multiplying the highest exponent prime factors of 509 and 510. First we will calculate the prime factors of 509 and 510.

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 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 509 and 510.

LCM(509,510) = 21×31×51×171×5091
LCM(509,510) = 259590

Factors of 509

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

1, 509

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 509 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 509 and 510, than apply into the LCM equation.

GCF(509,510) = 1
LCM(509,510) = ( 509 × 510) / 1
LCM(509,510) = 259590 / 1
LCM(509,510) = 259590

Properties of LCM 509 and 510

(i) The LCM of 510 and 509 is associative

LCM of 509 and 510 = LCM of 510 and 509

Related Least Common Multiples of 509

Related Least Common Multiples of 510

Frequently Asked Questions on LCM of 509 and 510

1. What is the LCM of 509 and 510?

Answer: LCM of 509 and 510 is 259590.

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 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 509 and 510?

Answer:

Least Common Multiple of 509 and 510 = 259590

Step 1: Find the prime factorization of 509

509 = 509

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 = 259590 = 2 x 3 x 5 x 17 x 509

Step 4: Therefore, the least common multiple of 509 and 510 is 259590.