Least Common Multiple of 513 and 519

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 513 and 519 the smallest integer that is 88749 that is divisible by both numbers.

Least Common Multiple (LCM) of 513 and 519 is 88749.

LCM(513,519) = 88749

LCM of 513 and 519

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

LCM of:
and

Least Common Multiple of 513 and 519

LCM of 513 and 519 is 88749

Least common multiple can be found by multiplying the highest exponent prime factors of 513 and 519. First we will calculate the prime factors of 513 and 519.

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

Prime Factorization of 519


3 519
173 173
1

Prime factors of 519 are 3,173. Prime factorization of 519 in exponential form is:

519 = 31×1731

Now multiplying the highest exponent prime factors to calculate the LCM of 513 and 519.

LCM(513,519) = 33×191×1731
LCM(513,519) = 88749

Factors of 513

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

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

Factors of 519

List of positive integer factors of 519 that divides 519 without a remainder.

1, 3, 173, 519

Least Common Multiple of 513 and 519 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 513 and 519, than apply into the LCM equation.

GCF(513,519) = 3
LCM(513,519) = ( 513 × 519) / 3
LCM(513,519) = 266247 / 3
LCM(513,519) = 88749

Properties of LCM 513 and 519

(i) The LCM of 519 and 513 is associative

LCM of 513 and 519 = LCM of 519 and 513

Related Least Common Multiples of 513

Related Least Common Multiples of 519

Frequently Asked Questions on LCM of 513 and 519

1. What is the LCM of 513 and 519?

Answer: LCM of 513 and 519 is 88749.

2. 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.

3. What are the Factors of 519?

Answer: Factors of 519 are 1, 3, 173, 519. There are 4 integers that are factors of 519. The greatest factor of 519 is 519.

4. How to Find the LCM of 513 and 519?

Answer:

Least Common Multiple of 513 and 519 = 88749

Step 1: Find the prime factorization of 513

513 = 3 x 3 x 3 x 19

Step 2: Find the prime factorization of 519

519 = 3 x 173

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

LCM = 88749 = 3 x 3 x 3 x 19 x 173

Step 4: Therefore, the least common multiple of 513 and 519 is 88749.