Least Common Multiple of 513 and 520

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 520 the smallest integer that is 266760 that is divisible by both numbers.

Least Common Multiple (LCM) of 513 and 520 is 266760.

LCM(513,520) = 266760

LCM of 513 and 520

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

LCM of:
and

Least Common Multiple of 513 and 520

LCM of 513 and 520 is 266760

Least common multiple can be found by multiplying the highest exponent prime factors of 513 and 520. First we will calculate the prime factors of 513 and 520.

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 520


2 520
2 260
2 130
5 65
13 13
1

Prime factors of 520 are 2, 5,13. Prime factorization of 520 in exponential form is:

520 = 23×51×131

Now multiplying the highest exponent prime factors to calculate the LCM of 513 and 520.

LCM(513,520) = 23×33×51×131×191
LCM(513,520) = 266760

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 520

List of positive integer factors of 520 that divides 520 without a remainder.

1, 2, 4, 5, 8, 10, 13, 20, 26, 40, 52, 65, 104, 130, 260, 520

Least Common Multiple of 513 and 520 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 520, than apply into the LCM equation.

GCF(513,520) = 1
LCM(513,520) = ( 513 × 520) / 1
LCM(513,520) = 266760 / 1
LCM(513,520) = 266760

Properties of LCM 513 and 520

(i) The LCM of 520 and 513 is associative

LCM of 513 and 520 = LCM of 520 and 513

Related Least Common Multiples of 513

Related Least Common Multiples of 520

Frequently Asked Questions on LCM of 513 and 520

1. What is the LCM of 513 and 520?

Answer: LCM of 513 and 520 is 266760.

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 520?

Answer: Factors of 520 are 1, 2, 4, 5, 8, 10, 13, 20, 26, 40, 52, 65, 104, 130, 260, 520. There are 16 integers that are factors of 520. The greatest factor of 520 is 520.

4. How to Find the LCM of 513 and 520?

Answer:

Least Common Multiple of 513 and 520 = 266760

Step 1: Find the prime factorization of 513

513 = 3 x 3 x 3 x 19

Step 2: Find the prime factorization of 520

520 = 2 x 2 x 2 x 5 x 13

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

LCM = 266760 = 2 x 2 x 2 x 3 x 3 x 3 x 5 x 13 x 19

Step 4: Therefore, the least common multiple of 513 and 520 is 266760.