Least Common Multiple of 510 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 510 and 513 the smallest integer that is 87210 that is divisible by both numbers.

Least Common Multiple (LCM) of 510 and 513 is 87210.

LCM(510,513) = 87210

LCM of 510 and 513

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

LCM of:
and

Least Common Multiple of 510 and 513

LCM of 510 and 513 is 87210

Least common multiple can be found by multiplying the highest exponent prime factors of 510 and 513. First we will calculate the prime factors of 510 and 513.

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

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 510 and 513.

LCM(510,513) = 21×33×51×171×191
LCM(510,513) = 87210

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

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 510 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 510 and 513, than apply into the LCM equation.

GCF(510,513) = 3
LCM(510,513) = ( 510 × 513) / 3
LCM(510,513) = 261630 / 3
LCM(510,513) = 87210

Properties of LCM 510 and 513

(i) The LCM of 513 and 510 is associative

LCM of 510 and 513 = LCM of 513 and 510

Related Least Common Multiples of 510

Related Least Common Multiples of 513

Frequently Asked Questions on LCM of 510 and 513

1. What is the LCM of 510 and 513?

Answer: LCM of 510 and 513 is 87210.

2. 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.

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 510 and 513?

Answer:

Least Common Multiple of 510 and 513 = 87210

Step 1: Find the prime factorization of 510

510 = 2 x 3 x 5 x 17

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 = 87210 = 2 x 3 x 3 x 3 x 5 x 17 x 19

Step 4: Therefore, the least common multiple of 510 and 513 is 87210.